## MCQ (Single Correct Answer)

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...

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $$\lambda$$. An alpha particle having certain kinetic energ...

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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 ...

The ratio of de-Broglie wavelength of an $$\alpha$$ particle and a proton accelerated from rest by the same potential is $$\frac{1}{\sqrt m}$$, the va...

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

An $$\alpha$$-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavel...

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

An $$\alpha$$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two...

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...

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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 equation $$\lambda=\frac{1.227}{x} \mathrm{~nm}$$ can be used to find the de-Brogli wavelength of an electron. In this equation $$x$$ stands for :...

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...

A parallel beam of light of wavelength $$900 \mathrm{~nm}$$ and intensity $$100 \,\mathrm{Wm}^{-2}$$ is incident on a surface perpendicular to the bea...

The ratio of wavelengths of proton and deuteron accelerated by potential Vp and Vd is 1 : $$\sqrt2$$. Then the ratio of Vp to Vd will be :...

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)

A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be :
(Take ...

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...

Let K1 and K2 be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength $$\lambda$$1 and $$\lambda$$2, res...

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

The de Broglie wavelengths for an electron and a photon are $$\lambda$$e and $$\lambda$$p respectively. For the same kinetic energy of electron and ph...

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An $$\alpha$$ particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths $$({\lambda _\alpha }:{\lambda _{C12}...

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 :
(...

Which is the correct ascending order of wavelengths?

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....

An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are Ee and pe a...

A proton, a neutron, an electron and an $$\alpha$$ particle have same energy. If $$\lambda$$p, $$\lambda$$n, $$\lambda$$e and $$\lambda$$a are the de ...

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 :

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...

A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option...

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 ...

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electro...

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

An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of p...

What should be the order of arrangement of de-Broglie wavelength of electron ($$\lambda$$e), an $$\alpha$$-particle ($$\lambda$$a) and proton ($$\lamb...

A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavel...

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...

An electron of mass me and a proton of mass mp are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associate...

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 speed of electrons in a scanning electron microscope is 1 $$\times$$ 107 ms-1. If the protons having the same speed are used instead of electrons,...

The decay of a proton to neutron is :

A proton and an $$\alpha$$-particle, having kinetic energies Kp and K$$\alpha$$ respectively, enter into a magnetic field at right angles.The ratio of...

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 particle is travelling 4 time as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the ma...

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?

An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is : (c being the velocity of light)

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

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should n...

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 ...

An electron of mass me and a proton of mass mp = 1836 me are moving with the same speed. The ratio of their de Broglie wavelength $${{{}^\lambda elect...

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...

The de-Broglie wavelength of a proton and $$\alpha$$-particle are equal. The ratio of their velocities is :

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...

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}...

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 $...

An electron (mass m) with initial velocity $$\overrightarrow v = {v_0}\widehat i + {v_0}\widehat j$$ is in an electric field $$\overrightarrow E = ...

When photon of energy 4.0 eV strikes the
surface of a metal A, the ejected photoelectrons
have maximum kinetic energy TA eV end
de-Broglie wavelength ...

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

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...

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...

Both the nucleus and the atom of some element arein their respective first excited states. They get de-excted by emitting photons of wavelengths $$\la...

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...

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 ...

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 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...

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 ...

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

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

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 ...

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...

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

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...

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...

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...

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...

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...

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...

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

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

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 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...

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 ...

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...

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

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

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

Which of the following atoms has the lowest ionization potential ?

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

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...

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

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...

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

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

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...

## Numerical

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...

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 ?...

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 particle of mass 9.1 $$\times$$ 10$$-$$31 kg travels in a medium with a speed of 106 m/s and a photon of a radiation of linear momentum 10$$-$$27 kg...

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

The wavelength of an X-ray beam is 10$$\mathop A\limits^o $$. The mass of a fictitious particle having the same energy as that of the X-ray photons is...

When radiation of wavelength $$\lambda $$ is used to
illuminate a metallic surface, the stopping
potential is V. When the same surface is
illuminated ...

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...