Atoms and Nuclei · Physics · JEE Main

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $$2: 1$$. After disintegration they will move :

The energy released in the fusion of $$2 \mathrm{~kg}$$ of hydrogen deep in the sun is $$E_H$$ and the energy released in the fission of $$2 \mathrm{~...

A hydrogen atom in ground state is given an energy of $$10.2 \mathrm{~eV}$$. How many spectral lines will be emitted due to transition of electrons?...

The energy equivalent of $$1 \mathrm{~g}$$ of substance is :

If $$M_0$$ is the mass of isotope $${ }_5^{12} B, M_p$$ and $$M_n$$ are the masses of proton and neutron, then nuclear binding energy of isotope is:...

In a hypothetical fission reaction $${ }_{92} X^{236} \rightarrow{ }_{56} \mathrm{Y}^{141}+{ }_{36} Z^{92}+3 R$$ The identity of emitted particles (R)...

Binding energy of a certain nucleus is $$18 \times 10^8 \mathrm{~J}$$. How much is the difference between total mass of all the nucleons and nuclear m...

The longest wavelength associated with Paschen series is : (Given $$\mathrm{R}_{\mathrm{H}}=1.097 \times 10^7 \mathrm{SI}$$ unit)

The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :

The angular momentum of an electron in a hydrogen atom is proportional to : (Where $$\mathrm{r}$$ is the radius of orbit of electron)

An electron rotates in a circle around a nucleus having positive charge $$\mathrm{Ze}$$. Correct relation between total energy (E) of electron to its ...

According to Bohr's theory, the moment of momentum of an electron revolving in $$4^{\text {th }}$$ orbit of hydrogen atom is:

Which of the following nuclear fragments corresponding to nuclear fission between neutron $$\left({ }_0^1 \mathrm{n}\right)$$ and uranium isotope $$\l...

From the statements given below : (A) The angular momentum of an electron in $n^{\text {th }}$ orbit is an integral multiple of $\hbar$. (B) Nuclear f...

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is :

If the wavelength of the first member of Lyman series of hydrogen is $$\lambda$$. The wavelength of the second member will be

An electron revolving in $$n^{\text {th }}$$ Bohr orbit has magnetic moment $$\mu_n$$. If $$\mu_n \propto n^x$$, the value of $$x$$ is

In a nuclear fission reaction of an isotope of mass $$M$$, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in te...

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5th excited state of a hydrogen atom is :...

Given below are two statements: Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the elec...

The explosive in a Hydrogen bomb is a mixture of $${ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3$$ and $${ }_3 \mathrm{Li}^6$$ in some condensed form. The cha...

The atomic mass of $${ }_6 \mathrm{C}^{12}$$ is $$12.000000 \mathrm{~u}$$ and that of $${ }_6 \mathrm{C}^{13}$$ is $$13.003354 \mathrm{~u}$$. The requ...

The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is:

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$ Assertion A : The bindi...

$$_{92}^{238}A \to _{90}^{234}B + _2^4D + Q$$ In the given nuclear reaction, the approximate amount of energy released will be: [Given, mass of $${ }_...

A $$12.5 \mathrm{~eV}$$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

The energy of $$\mathrm{He}^{+}$$ ion in its first excited state is, (The ground state energy for the Hydrogen atom is $$-13.6 ~\mathrm{eV})$$ :...

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $$\lambda_{A}$$ and $$\l...

The half life of a radioactive substance is T. The time taken, for disintegrating $$\frac{7}{8}$$th part of its original mass will be:

The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in...

A radio active material is reduced to $$1 / 8$$ of its original amount in 3 days. If $$8 \times 10^{-3} \mathrm{~kg}$$ of the material is left after 5...

The waves emitted when a metal target is bombarded with high energy electrons are

For a nucleus $${ }_{\mathrm{A}}^{\mathrm{A}} \mathrm{X}$$ having mass number $$\mathrm{A}$$ and atomic number $$\mathrm{Z}$$ A. The surface energy pe...

A small particle of mass $$m$$ moves in such a way that its potential energy $$U=\frac{1}{2} m ~\omega^{2} r^{2}$$ where $$\omega$$ is constant and $$...

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is : ...

An electron of a hydrogen like atom, having $$Z=4$$, jumps from $$4^{\text {th }}$$ energy state to $$2^{\text {nd }}$$ energy state. The energy relea...

The mass of proton, neutron and helium nucleus are respectively $$1.0073~u,1.0087~u$$ and $$4.0015~u$$. The binding energy of helium nucleus is :...

The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A: The nuclear d...

Speed of an electron in Bohr's $$7^{\text {th }}$$ orbit for Hydrogen atom is $$3.6 \times 10^{6} \mathrm{~m} / \mathrm{s}$$. The corresponding speed ...

Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of $$\frac{1}{2}$$ day. If b...

If a radioactive element having half-life of $$30 \mathrm{~min}$$ is undergoing beta decay, the fraction of radioactive element remains undecayed afte...

The energy levels of an atom is shown in figure. Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm? Given...

The ratio of the density of oxygen nucleus ($$_8^{16}O$$) and helium nucleus ($$_2^{4}\mathrm{He}$$) is

A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 $$\tim...

Consider the following radioactive decay process $$_{84}^{218}A\buildrel \alpha \over \longrightarrow {A_1}\buildrel {{\beta ^ - }} \over \longrigh...

Read the following statements : (A) Volume of the nucleus is directly proportional to the mass number. (B) Volume of the nucleus is independent of mas...

Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the fir...

A radioactive sample decays $$\frac{7}{8}$$ times its original quantity in 15 minutes. The half-life of the sample is

The half life period of a radioactive substance is 60 days. The time taken for $$\frac{7}{8}$$th of its original mass to disintegrate will be :

The activity of a radioactive material is $$6.4 \times 10^{-4}$$ curie. Its half life is 5 days. The activity will become $$5 \times 10^{-6}$$ curie a...

What is the half-life period of a radioactive material if its activity drops to $$1 / 16^{\text {th }}$$ of its initial value in 30 years?

A nucleus of mass $$M$$ at rest splits into two parts having masses $$\frac{M^{\prime}}{3}$$ and $${{2M'} \over 3}(M' ...

Mass numbers of two nuclei are in the ratio of $$4: 3$$. Their nuclear densities will be in the ratio of

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 dis...

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $$\lambda$$. The value of principal quantum number '$$n$...

The momentum of an electron revolving in $$\mathrm{n}^{\text {th }}$$ orbit is given by : (Symbols have their usual meanings)

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by :

A hydrogen atom in ground state absorbs 12.09 eV of energy. The orbital angular momentum of the electron is increased by :

In the following nuclear reaction, $$D\buildrel \alpha \over \longrightarrow {D_1}\buildrel {{\beta ^ - }} \over \longrightarrow {D_2}\buildrel \al...

The activity of a radioactive material is 2.56 $$\times$$ 10$$-$$3 Ci. If the half life of the material is 5 days, after how many days the activity wi...

Following statements related to radioactivity are given below : (A) Radioactivity is a random and spontaneous process and is dependent on physical and...

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, Kp are related as :

Given below are two statements : Statement I : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (E1...

A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of : (...

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process....

How many alpha and beta particles are emitted when Uranium 92U238 decays to lead 82Pb206 ?

Which of the following figure represents the variation of $${l_n}\left( {{R \over {{R_0}}}} \right)$$ with $${l_n}A$$ (if R = radius of a nucleus and ...

The ratio for the speed of the electron in the 3rd orbit of He+ to the speed of the electron in the 3rd orbit of hydrogen atom will be :...

In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the ...

Choose the correct option from the following options given below :

Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115....

The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of a...

A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot o...

There are 1010 radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? $$\lef...

At time t = 0, a material is composed of two radioactive atoms A and B, where NA(0) = 2NB(0). The decay constant of both kind of radioactive atoms is ...

A particular hydrogen like ion emits radiation of frequency 2.92 $$\times$$ 1015 Hz when it makes transition from n = 3 to n = 1. The frequency in Hz ...

Consider the following statements :A. Atoms of each element emit characteristics spectrum.B. According to Bohr's Postulate, an electron in a hydrogen ...

If 'f' denotes the ratio of the number of nuclei decayed (Nd) to the number of nuclei at t = 0 (N0) then for a collection of radioactive nuclei, the r...

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed a...

The half-life of $${}^{198}Au$$ is 3 days. If atomic weight of $${}^{198}Au$$ is 198 g/mol then the activity of 2 mg of $${}^{198}Au$$ is [in disinteg...

A nucleus with mass number 184 initially at rest emits an $$\alpha$$-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy...

For a certain radioactive process the graph between In R and t(sec) is obtained as shown in the figure. Then the value of half life for the unknown ra...

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the ti...

A nucleus of mass M emits $$\gamma$$ -ray photon of frequency 'v'. The loss of internal energy by the nucleus is :[Take 'c' as the speed of electromag...

The decay of a proton to neutron is :

Imagine that the electron in a hydrogen atom is replaced by a muon ($$\mu$$). The mass of muon particle is 207 times that of an electron and charge is...

A radioactive sample disintegrates via two independent decay processes having half lives $$T_{1/2}^{(1)}$$ and $$T_{1/2}^{(2)}$$ respectively. The eff...

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

If an electron is moving in the nth orbit of the hydrogen atom, then its velocity (vn) for the nth orbit is given as :...

Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

The half-life of Au198 is 2.7 days. The activity of 1.50 mg of Au198 if its atomic weight is 198 g mol$$-$$1 is, (Na = 6 $$\times$$ 1023/mol)....

A radioactive sample is undergoing $$\alpha$$ decay. At any time t1, its activity is A and another time t2, the activity is $${A \over 5}$$. What is t...

If $$\lambda$$1 and $$\lambda$$2 are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value ...

The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is :

Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half life of X is half of the half life of Y. After three half lives...

According to Bohr atomic model, in which of the following transitions will the frequency be maximum?

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E.The transitions A, B and C...

Given the masses of various atomic particles mp = 1.0072 u, mn = 1.0087 u, me = 0.000548 u, $${m_{\overline v }}$$ = 0, md = 2.0141 u, where p $$ \equ...

You are given that Mass of $${}_3^7Li$$ = 7.0160u, Mass of $${}_2^4He$$ = 4.0026u and Mass of $${}_1^1H$$ = 1.0079u. When 20 g of $${}_3^7Li$$ is conv...

A radioactive nucleus decays by two different processes. The half life for the first process is 10 s and that for the second is 100 s. The effective h...

Activities of three radioactive substances A, B and C are represented by the curves A, B and C, in the figure. Then their half-lives $${T_{{1 \over 2}...

Find the Binding energy per neucleon for $${}_{50}^{120}Sn$$. Mass of proton mp = 1.00783 U, mass of neutron mn = 1.00867 U and mass of tin nucleus ...

The radius R of a nucleus of mass number A can be estimated by the formula R = (1.3 $$ \times $$ 10–15)A1/3 m. It follows that the mass density of a n...

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen a...

In a radioactive material, fraction of active material remaining after time t is 9/16. The fraction that was remaining after t/2 is

In a hydrogen atom the electron makes a transition from (n + 1)th level to the nth level. If n >> 1, the frequency of radiation emitted is propo...

In a reactor, 2 kg of 92U235 fuel is fully used up in 30 days. The energy released per fission is 200 MeV. Given that the Avogadro number, N = 6.023 $...

The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron...

The graph which depicts the results of Rutherford gold foil experiment with $$\alpha $$-particales is : $$\theta $$ : Scattering angle Y : Number of s...

The activity of a radioactive sample falls from 700 s–1 to 500 s–1 in 30 minutes. Its half life is close to:

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 $$ \times $$ 10-16 s. The frequency of revolution of the...

Consider an electron in a hydrogen atom revolving in its second excited state (having radius 4.65 $$\mathop A\limits^o $$). The de-Broglie wavelength ...

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ...

Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively, If initially a sample has equal number of nuclei, then after...

An excited He+ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number...

Two radioactive substances A and B have decay constants 5$$\lambda $$ and $$\lambda $$ respectively. At t = 0, a sample has the same number of the two...

In Li+ +, electron in first Bohr orbit is excited to a level by a radiation of wavelength $$\lambda $$. When the ion gets deexcited to the ground stat...

Two radioactive materials A and B have decay constants 10$$\lambda $$ and $$\lambda $$, respectively. It initially they have the same number of nuclei...

A He+ ion is in its first excited state. Its ionization energy is :-

Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) wil...

The ratio of mass densities of nuclei of 40Ca and 16O is close to :-

Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He+ ions in n = 1 and n = 2 states. The possible transition of helium ions ...

In a radioactive decay chain, the initial nucleus is $${}_{90}^{232}$$Th. At the end there are 6 $$\alpha $$-particles and 4 $$\beta $$-particles whic...

A particle of mass m moves in a circular orbit in a central potential field U(r) = $${1 \over 2}$$ kr2. If Bohr 's quantization conditions are applied...

In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is $$\lambda $$. If an electron j...

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980$$\mathop A\limits^ \circ $$. The radius of the atom...

Consider the nuclear fission Ne20 $$ \to $$ 2He4 + C12 Given that the binding energy/ nucleon of Ne20, He4 and C12 are, respectively, 8.03 MeV, ...

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 se...

At a given instant, say t = 0, two radioactive substance A and B have equal activities. the ratio $${{{R_B}} \over {{R_A}}}$$ of their activities aft...

A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 $$ \times $$ 1010 decays/s), has twice the number of nuclei as another s...

At some instant, a radioactive sample S1 having an activity 5 $$\mu $$Ci has twice the number of nuclei as another sample S2 which has an activity of...

If the series limit frequency of the Lyman series is $${\nu _L}$$, then the series limit frequency of the Pfund series is:

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is pd; while for its simila...

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let $${\lambda _n}$$, $${\lambda _g}$$ be the de ...

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei ...

Muon ($$\mu $$$$-$$) is a negatively charged (|q| = |e|) particle with a mass m$$\mu $$ = 200 me, where me is the mass of the electron and e is the el...

A solution containing active cobalt $${^{60}_{27}}Co$$ having activity of $$0.8$$ $$\mu Ci$$ and decay constant $$\lambda $$ is injected in an animal'...

The energy required to remove the electron from a singly ionized Helium atom is $$2.2$$ times the energies required to remove an electron from Helium ...

Imagine that a reactor converts all given mass into energy and that it operates at a power level of 109 watt. The mass of the fuel consumed per hour ...

The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :

Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1...

According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the nth...

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = $${{\lambda _1}}$$/$${{\lambda _2}}$$, is given by: ...

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to t...

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state ...

Half-lives of two radioactive elements $$A$$ and $$B$$ are $$20$$ minutes and $$40$$ minutes, respectively. Initially, the samples have equal number o...

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

Hydrogen $$\left( {{}_1{H^1}} \right)$$, Deuterium $$\left( {{}_1{H^2}} \right)$$, singly ionised Helium $${\left( {{}_2H{e^4}} \right)^ + }$$ and dou...

The radiation corresponding to $$3 \to 2$$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to...

In a hydrogen like atom electron make transition from an energy level with quantum number $$n$$ to another with quantum number $$\left( {n - 1} \right...

Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutron $$ = 1.6725 \times {10^{ - ...

A diatomic molecule is made of two masses $${m_1}$$ and $${m_2}$$ which are separated by a distance $$r.$$ If we calculate its rotational energy by ap...

Hydrogen atom is excited from ground state to another state with principal quantum number equal to $$4.$$ Then the number of spectral lines in the emi...

Energy required for the electron excitation in $$L{i^{ + + }}$$ from the first to the third Bohr orbit is :

The half life of a radioactive substance is $$20$$ minutes. The approximate time interval $$\left( {{t_2} - {t_1}} \right)$$ between the time $${{t_2}...

A nucleus of mass $$M+$$$$\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $${M \over 2}$$ each. Speed of light is $$c.$$ The ...

A nucleus of mass $$M+$$$$\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $${M \over 2}$$ each. Speed of light is $$c.$$ The ...

A radioactive nucleus (initial mass number $$A$$ and atomic number $$Z$$ emits $$3\,\alpha $$- particles and $$2$$ positrons. The ratio of number of n...

The transition from the state $$n=4$$ to $$n=3$$ in a hydrogen like atom result in ultra violet radiation. Infrared radiation will be obtained in the...

The above is a plot of binding energy per nucleon $${E_b},$$ against the nuclear mass $$M;A,B,C,D,E,F$$ correspond to different nuclei. Consider fou...

Suppose an electron is attracted towards the origin by a force $${k \over r}$$ where $$'k'$$ is a constant and $$'r'$$ is the distance of the electron...

This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one that best describes the two sta...

If $${M_O}$$ is the mass of an oxygen isotope $${}_8{O^{17}}$$ , $${M_p}$$ and $${M_N}$$ are the masses of a proton and neutron respectively, the nucl...

In gamma ray emission from a nucleus

The half-life period of a ratio-active element $$X$$ is same as the mean life time of another ratio-active element $$Y.$$ Initially they have the same...

Which of the following transitions in hydrogen atoms emit photons of highest frequency ?

An alpha nucleus of energy $${1 \over 2}m{v^2}$$ bombards a heavy nuclear target of charge $$Ze$$. Then the distance of closest approach for the alpha...

When $${}_3L{i^7}$$ nuclei are bombarded by protons, and the resultant nuclei are $${}_4B{e^8}$$, the emitted particles will be

If the binding energy per nucleon in $${}_3^7Li$$ and $${}_2^4He$$ nuclei are $$5.60$$ $$MeV$$ and $$7.06$$ $$MeV$$ respectively, then in the reaction...

The $$'rad'$$ is the correct unit used to report the measurement of

The energy spectrum of $$\beta $$-particles [ number $$N(E)$$ as a function of $$\beta $$-energy $$E$$ ] emitted from a radioactive source is

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy...

A nuclear transformation is denoted by $$X\left( {n,\alpha } \right)\matrix{ 7 \cr 3 \cr } Li.$$ Which of the following is the nucleus of ...

If radius of the $$\matrix{ {27} \cr {13} \cr } $$ $$Al$$ nucleus is estimated to be $$3.6$$ fermi then the radius of $$\matrix{ {125} ...

The intensity of gamma radiation from a given source is $$L$$. On passing through $$36$$ $$mm$$ of lead, it is reduced to $${{\rm I} \over 8}.$$ The t...

Starting with a sample of pure $${}^{66}Cu,{7 \over 8}$$ of it decays into $$Zn$$ in $$15$$ minutes. The corresponding half life is

The binding energy per nucleon of deuteron $$\left( {{}_1^2\,H} \right)$$ and helium nucleus $$\left( {{}_2^4\,He} \right)$$ is $$1.1$$ $$MeV$$ and $$...

A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of $$2:1.$$ The ratio of their nuclear sizes will be

An $$\alpha $$-particle of energy $$5$$ $$MeV$$ is scattered through $${180^ \circ }$$ by a fixed uranium nucleus. The distance of closest approach is...

Which of the following radiations has the least wavelength ?

When a $${U^{238}}$$ nucleus originally at rest, decays by emitting an alpha particle having a speed $$'u',$$ the recoil speed of the residual nucleus...

A nucleus with $$Z=92$$ emits the following in a sequence: $$$\alpha ,{\beta ^ - },{\beta ^ - },\alpha ,\alpha ,\alpha ,\alpha ,\alpha ,{\beta ^ - },...

A radioactive sample at any instant has its disintegration rate $$5000$$ disintegrations per minute. After $$5$$ minutes, the rate is $$1250$$ disinte...

The wavelengths involved in the spectrum of deuterium $$\left( {{}_1^2\,D} \right)$$ are slightly different from that of hydrogen spectrum, because

If the binding energy of the electron in a hydrogen atom is $$13.6eV,$$ the energy required to remove the electron from the first excited state of $$L...

Which of the following cannot be emitted by radioactive substances during their decay ?

Which of the following atoms has the lowest ionization potential ?

In the nuclear fusion reaction $$${}_1^2H + {}_1^3H \to {}_2^4He + n$$$ given that the repulsive potential energy between the two nuclei is $$ \sim 7...

At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit $$\eqalign{ & \left( i \right)\,...

If $$13.6$$ $$eV$$ energy is required to ionize the hydrogen atom, then the energy required to remove an electron from $$n=2$$ is

If $${N_0}$$ is the original mass of the substance of half-life period $${t_{1/2}} = 5$$ years, then the amount of substance left after $$15$$ years i...

A star has $$100 \%$$ helium composition. It starts to convert three $${ }^4 \mathrm{He}$$ into one $${ }^{12} \mathrm{C}$$ via triple alpha process a...

In an alpha particle scattering experiment distance of closest approach for the $$\alpha$$ particle is $$4.5 \times 10^{-14} \mathrm{~m}$$. If target ...

Radius of a certain orbit of hydrogen atom is 8.48 $$\mathop A\limits^o$$. If energy of electron in this orbit is $$E / x$$. then $$x=$$ ________ (Giv...

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $$915\mathop A\limits^o$$. The longest wavelength of spectra...

If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is ________ $$\times 10^{-2} \mathrm{~MeV}$$. (Given...

The disintegration energy $$Q$$ for the nuclear fission of $${ }^{235} \mathrm{U} \rightarrow{ }^{140} \mathrm{Ce}+{ }^{94} \mathrm{Zr}+n$$ is _______...

A hydrogen atom changes its state from $$n=3$$ to $$n=2$$. Due to recoil, the percentage change in the wave length of emitted light is approximately $...

A particular hydrogen-like ion emits the radiation of frequency $3 \times 10^{15} \mathrm{~Hz}$ when it makes transition from $n=2$ to $n=1$. The freq...

The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$, where $x...

A nucleus has mass number $$A_1$$ and volume $$V_1$$. Another nucleus has mass number $$A_2$$ and Volume $$V_2$$. If relation between mass number is $...

The mass defect in a particular reaction is $$0.4 \mathrm{~g}$$. The amount of energy liberated is $$n \times 10^7 \mathrm{~kWh}$$, where $$n=$$ _____...

A electron of hydrogen atom on an excited state is having energy $$\mathrm{E}_{\mathrm{n}}=-0.85 \mathrm{~eV}$$. The maximum number of allowed transit...

Hydrogen atom is bombarded with electrons accelerated through a potential difference of $$\mathrm{V}$$, which causes excitation of hydrogen atoms. If ...

When a hydrogen atom going from $$n=2$$ to $$n=1$$ emits a photon, its recoil speed is $$\frac{x}{5} \mathrm{~m} / \mathrm{s}$$. Where $$x=$$ ________...

If Rydberg's constant is $$R$$, the longest wavelength of radiation in Paschen series will be $$\frac{\alpha}{7 R}$$, where $$\alpha=$$ ________....

In a nuclear fission process, a high mass nuclide $$(A \approx 236)$$ with binding energy $$7.6 \mathrm{~MeV} /$$ Nucleon dissociated into middle mass...

As per given figure $A, B$ and $C$ are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavele...

The radius of $$2^{\text {nd }}$$ orbit of $$\mathrm{He}^{+}$$ of Bohr's model is $$r_{1}$$ and that of fourth orbit of $$\mathrm{Be}^{3+}$$ is repres...

A common example of alpha decay is $${ }_{92}^{238} \mathrm{U} \longrightarrow{ }_{90}^{234} \mathrm{Th}+{ }_{2} \mathrm{He}^{4}+\mathrm{Q}$$ Given : ...

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $$1: 2^{1 / 3}$$. Their respective speed have a rat...

If 917 $$\mathop A\limits^o $$ be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be ___________ $$\mathop A\li...

The decay constant for a radioactive nuclide is 1.5 $$\times$$ 10$$^{-5}$$ s$$^{-1}$$. Atomic weight of the substance is 60 g mole$$^{-1}$$, ($$N_A=6\...

The ratio of wavelength of spectral lines $$\mathrm{H}_{\alpha}$$ and $$\mathrm{H}_{\beta}$$ in the Balmer series is $$\frac{x}{20}$$. The value of $$...

A nucleus with mass number 242 and binding energy per nucleon as $$7.6~ \mathrm{MeV}$$ breaks into two fragment each with mass number 121. If each fra...

Experimentally it is found that $$12.8 ~\mathrm{eV}$$ energy is required to separate a hydrogen atom into a proton and an electron. So the orbital rad...

The radius of fifth orbit of the $$\mathrm{Li}^{++}$$ is __________ $$\times 10^{-12} \mathrm{~m}$$. Take: radius of hydrogen atom $$ = 0.51\,\mathop ...

Nucleus A having $$Z=17$$ and equal number of protons and neutrons has $$1.2 ~\mathrm{MeV}$$ binding energy per nucleon. Another nucleus $$\mathrm{B}$...

A light of energy $$12.75 ~\mathrm{eV}$$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its ...

If the binding energy of ground state electron in a hydrogen atom is $13.6\, \mathrm{eV}$, then, the energy required to remove the electron from the s...

For hydrogen atom, $$\lambda_{1}$$ and $$\lambda_{2}$$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. T...

A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is $30 \mathrm{~...

A radioactive element $$_{92}^{242}$$X emits two $$\alpha$$-particles, one electron and two positrons. The product nucleus is represented by $$_{\math...

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be $${\left( {{x...

The wavelength of the radiation emitted is $$\lambda_0$$ when an electron jumps from the second excited state to the first excited state of hydrogen a...

The energy released per fission of nucleus of $$^{240}$$X is 200 MeV. The energy released if all the atoms in 120g of pure $$^{240}$$X undergo fission...

Assume that protons and neutrons have equal masses. Mass of a nucleon is $$1.6\times10^{-27}$$ kg and radius of nucleus is $$1.5\times10^{-15}~\mathrm...

Two radioactive materials A and B have decay constants $$25 \lambda$$ and $$16 \lambda$$ respectively. If initially they have the same number of nucle...

A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, ...

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below : $${ }_{1}^{2} X+{ }_{1}^{2} X={ }_{2}^{4} Y$$ The bin...

In the hydrogen spectrum, $$\lambda$$ be the wavelength of first transition line of Lyman series. The wavelength difference will be "a$$\lambda$$'' be...

$${x \over {x + 4}}$$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) third permitted ener...

A hydrogen atom in its first excited state absorbs a photon of energy x $$\times$$ 10$$-$$2 eV and excited to a higher energy state where the potentia...

The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial va...

$$\sqrt {{d_1}} $$ and $$\sqrt {{d_2}} $$ are the impact parameters corresponding to scattering angles 60$$^\circ$$ and 90$$^\circ$$ respectively, whe...

A beam of monochromatic light is used to excite the electron in Li+ + from the first orbit to the third orbit. The wavelength of monochromatic light i...

A sample contains 10$$-$$2 kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The...

X different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number n = 6 ?...

The K$$\alpha$$ X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atoms with a K electron knocked out is 27.5 keV, the energy...

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 $$\mathop A\limits^o $$. If the speed of electron is 2.2 ...

A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 $$\mu$$F is first charged and later connected with r...

From the given data, the amount of energy required to break the nucleus of aluminium $$_{13}^{27}$$Al is __________ x $$\times$$ 10$$-$$3 J.Mass of ne...

The nuclear activity of a radioactive element becomes $${\left( {{1 \over 8}} \right)^{th}}$$ of its initial value in 30 years. The half-life of radio...

A radioactive substance decays to $${\left( {{1 \over {16}}} \right)^{th}}$$ of its initial activity in 80 days. The half life of the radioactive subs...

A particle of mass m moves in a circular orbit in a central potential field U(r) = U0r4. If Bohr's quantization conditions are applied, radii of possi...

The first three spectral lines of H-atom in the Balmer series are given $$\lambda$$1, $$\lambda$$2, $$\lambda$$3 considering the Bohr atomic model, th...

A particle of mass 200 MeV/c2 collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goe...

The first member of the Balmer series of hydrogen atom has a wavelength of 6561 Å. The wavelength of the second member of the Balmer series (in nm) is...