Atoms and Nuclei · Physics · MHT CET

In the second orbit of hydrogen atom, the energy of an electron is ' $E$ '. In the third orbit of helium atom, the energy of the electron will be (atomic number of helium $=2$)

Two radioactive substances A and B have decay constants ' $5 \lambda$ ' and ' $\lambda$ ' respectively. At $\mathrm{t}=0$, they have the same number of nuclei. The ratio of number of nuclei of $A$ to those of $B$ will be $\left(\frac{1}{\mathrm{e}}\right)^2$ after a time interval

In $\mathrm{M}_{\mathrm{O}}$ is the mass of an oxygen isotope ${ }_8 \mathrm{O}^{17}$ and $\mathrm{M}_{\mathrm{p}}$ and $\mathrm{M}_{\mathrm{N}}$ are the mass of proton and mass of neutron respectively, then the nucleus binding energy of the isotope is

Frequency of the series limit of Balmer series of hydrogen atom of Rydberg's constant ' $R$ ' and velocity of light ' $C$ ' is

Acceleration of an electron in the first Bohr's orbit is proportional to $\mathrm{m}=$ mass of electron, $\mathrm{r}=$ radius of the orbit, $\mathrm{h}=$ Planck's constant)

In the given reaction

$${ }_z \mathrm{X}^A \rightarrow{ }_{z+1} \mathrm{Y}^A \rightarrow{ }_{z-1} \mathrm{~K}^{A-4} \rightarrow{ }_{z-1} \mathrm{~K}^{\mathrm{A}-4}$$

radioactive radiations are emitted in the sequence

A radioactive substance has half-life of 60 minute. During 3 hour, the amount of substance decayed would be

The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is

In a hydrogen atom in its ground state, the first Bohr orbit has radius $r_1$. The electron's orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is

The angular momentum of the electron in the third Bohr orbit of hydrogen atom is ' $l$ '. Its angular momentum in the fourth Bohr orbit is

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (a) second to first energy level and (b) highest energy level to second level is

If 'T' is the half life of a radioactive substance then its instantaneous rate of change of activity is proportional to

Radius of first orbit in H -atom is ' $a_0$ ' Then, de-Broglie wavelength of electron in the third orbit is

In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If ' $r_0$ ' is the radius of the ground state orbit, ' $m$ ' is the mass, ' e ' is the charge on the electron and ' $\varepsilon_0$ ' is the permittivity of vacuum, the speed of the electron is

If the ionisation energy for the hydrogen atom is 13.6 eV , then the energy required to excite it from the ground state to the next higher state is nearly

Using Bohr's model, the orbital period of electron in hydrogen atom in $\mathrm{n}^{\text {th }}$ orbit is ( $\mathrm{m}=$ mass of electron, $\mathrm{h}=$ Planck's constant, $\mathrm{e}=$ electronic charge, $\varepsilon_0=$ permittivity of free space)

The spectral series observed for hydrogen atom found in visible region is

In hydrogen atom, if $\mathrm{V}_{\mathrm{n}}$ and $\mathrm{V}_{\mathrm{p}}$ are orbital velocities in $\mathrm{n}^{\text {th }}$ and $\mathrm{p}^{\text {th }}$ orbit respectively, then the ratio $\mathrm{V}_{\mathrm{p}}: \mathrm{V}_{\mathrm{n}}$ is

When a hydrogen atom is raised from the ground state to the excited state

In hydrogen atom, ratio of the shortest wavelength in the Balmer series to that in the Paschen series is

According to Bohr's theory of hydrogen atom, the ratio of the maximum and minimum wavelength of Lyman series will be

The ratio of minimum wavelengths of Lyman and Balmer series will be

Half-lives of two radioactive elements A and B are 30 minute and 60 minute respectively. Initially the samples have equal number of nuclei. After 120 minute the ratio of decayed numbers of nuclei of $B$ to that of $A$ will be

For hydrogen atom, ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of ' $\lambda_1$ ' and ' $\lambda_2$ ' is $\frac{x}{32}$. The value of ' $x$ ' is

The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is

A diatomic molecule has moment of inertia ' I ', By applying Bohr's quantization condition, its rotational energy in the $\mathrm{n}^{\text {th }}$ level is $[\mathrm{n} \geq 1]$ [h= Planck's constant]

In the uranium radioactive series, the initial nucleus is ${ }_{92}^{238} \mathrm{U}$ and that the final nucleus is ${ }_{82}^{206} \mathrm{~Pb}$. When uranium nucleus decays into lead, the number of $\alpha$-particles and $\beta$-particles emitted are

If ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths of the first line of the Lyman and Paschen series respectively, then $\lambda_2: \lambda_1$ is

An electron of stationary Hydrogen atom passes from fifth energy level to ground level. The velocity that the atom acquired as a result of photo emission is

( $\mathrm{m}=$ mass of electron, $\mathrm{R}=$ Rydberg's constant)

( $\mathrm{h}=$ Planck's constant)

Which of the following statements about the Bohr model of the hydrogen atom is false?

The radius of innermost orbit of hydrogen atom is $5.3 \times 10^{-11} \mathrm{~m}$. The radius of fourth allowed orbit of hydrogen atom is

In the third orbit of hydrogen atom the energy of an electron ' $E$ '. In the fifth orbit of helium $(Z=2)$ the energy of an electron will be

Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum is

Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be

Frequency of the series limit of Balmer series of hydrogen atom in terms of Rydberg's constant (R) and velocity of light (c) is

If the radius of the first Bohr orbit is '$$r$$' then the de-Broglie wavelength of the electron in the $$4^{\text {th }}$$ orbit will be

Magnetic field at the centre of the hydrogen atom due to motion of electron in $$\mathrm{n}^{\text {th }}$$ orbit is proportional to

An excited hydrogen atom emits a photon of wavelength $$\lambda$$ in returning to ground state. The quantum number $$n$$ of the excited state is ($$R=$$ Rydberg's constant)

When an electron is excited from its 4 th orbit to 5 th stationary orbit, the change in the angular momentum of electron is approximately.

(Planck's constant $$=h=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}$$ )

A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be

An isotope of the original nucleus can be formed in a radioactive decay, with the emission of following particles.

Two different radioactive elements with half lives '$$\mathrm{T}_1$$' and '$$\mathrm{T}_2$$' have undecayed atoms '$$\mathrm{N}_1$$' and '$$\mathrm{N}_2$$' respectively present at a given instant. The ratio of their activities at that instant is

In Balmer series, wavelength of the $$2^{\text {nd }}$$ line is '$$\lambda_1$$' and for Paschen series, wavelength of the $$1^{\text {st }}$$ line is '$$\lambda_2$$', then the ratio '$$\lambda_1$$' to '$$\lambda_2$$' is

In Lyman series, series limit of wavelength is $$\lambda_1$$. The wavelength of first line of Lyman series is $$\lambda_2$$ and in Balmer series, the series limit of wavelength is $$\lambda_3$$. Then the relation between $$\lambda_1$$, $$\lambda_2$$ and $$\lambda_3$$ is

The wavelength of radiation emitted is '$$\lambda_0$$' when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be $$\frac{20}{x} \lambda_0$$. The value of $$x$$ is

According to Bohr's theory of hydrogen atom, the total energy of the electron in the $$\mathrm{n}^{\text {th }}$$ stationary orbit is

Bohr model is applied to a particle of mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$' moving in a plane under the influence of a transverse magnetic field '$$B$$'. The energy of the charged particle in the $$\mathrm{n}^{\text {th }}$$ leve will be $$[\mathrm{h}=$$ Planck's constant $$]$$

The orbital magnetic moment associated with orbiting electron of charge '$$e$$' is

An electron in the hydrogen atom jumps from the first excited state to the ground state. What will be the percentage change in the speed of electron?

In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at time $$t=\frac{1}{2 \lambda}$$ is [$$\lambda=$$ decay constant]

The ratio of the velocity of the electron in the first Bohr orbit to that in the second Bohr orbit of hydrogen atom is

The shortest wavelength in the Balmer series of hydrogen atom is equal to the shortest wavelength in the Brackett series of a hydrogen like atom of atomic number $$\mathrm{z}$$. The value of $$\mathrm{z}$$ is

The ratio of longest to shortest wavelength emitted in Paschen series of hydrogen atom is

The force acting on the electron in hydrogen atom (Bohr' theory) is related to the principle quantum number '$$n$$' as

The wavelength of light for the least energetic photons emitted in the Lyman series of the hydrogen spectrum is nearly [Take $$\mathrm{hc}=1240 ~\mathrm{eV}$$ - $$\mathrm{nm}$$, change in energy of the levels $$=10.2 ~\mathrm{eV}$$ ]

The ratio of wavelengths for transition of electrons from $$2^{\text {nd }}$$ orbit to $$1^{\text {st }}$$ orbit of Helium $$\left(\mathrm{He}^{++}\right)$$ and Lithium $$\left(\mathrm{Li}^{++1}\right)$$ is (Atomic number of Helium $$=2$$, Atomic number of Lithium $$=3$$ )

For an electron moving in the $$\mathrm{n}^{\text {th }}$$ Bohr orbit the deBroglie wavelength of an electron is

If an electron in a hydrogen atom jumps from an orbit of level $$n=3$$ to orbit of level $$n=2$$, then the emitted radiation frequency is (where R = Rydberg's constant, C = Velocity of light)

Using Bohr's model, the orbital period of electron in hydrogen atom in the $$\mathrm{n}^{\text {th }}$$ orbit is $$\left(\varepsilon_0=\right.$$ permittivity of vacuum, $$\mathrm{h}=$$ Planck's constant, $$\mathrm{m}=$$ mass of electron, $$\mathrm{e}=$$ electronic charge)

The wave number of the last line of the Balmer series in hydrogen spectrum will be

(Rydberg's constant $$=10^7 \mathrm{~m}^{-1}$$ )

The half life of a radioactive substance is 30 minute. The time taken between 40% decay and 85% decay of the same radioactive substance is

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) second to first energy level and (ii) highest energy level to second energy level is

An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the following statements which one is correct?

The ratio of maximum to minimum wavelength in Balmer series of hydrogen atom is

Energy of electron in the second orbit of hydrogen atom is $$\mathrm{E}$$. The energy of electron '$$\mathrm{E}_3$$' in the third orbit of helium $$(\mathrm{He})$$ atom will be

The shortest wavelength for Lyman series is 912 $$\mathop A\limits^o $$. The longest wavelength in Paschen series is

In the Bohr model, an electron moves in a circular orbit around the nucleus. Considering an orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in nth excited state, is

(e = electronic charge, m$$_e$$ = mass of the electron, h = Planck's constant)

The energy of an electron in the excited hydrogen atom is $$-3.4 \mathrm{~eV}$$. Then according to Bohr's theory, the angular momentum of the electron in that excited state is ($$\mathrm{h}=$$ Plank's constant)

In $$n^{\text {th }}$$ Bohr orbit, the ratio of the kinetic energy of an electron to the total energy of it, is

If '$$E$$' and '$$L$$' denote the magnitude of total energy and angular momentum of revolving electron in $$\mathrm{n}^{\text {th }}$$ Bohr orbit, then

Two radioactive materials $$X_1$$ and $$X_2$$ have decay constants '$$5 \lambda$$' and '$$\lambda$$' respectively. Initially, they have the same number of nuclei. After time '$$t$$', the ratio of number of nuclei of $$X_1$$ to that of $$\mathrm{X}_2$$ is $$\frac{1}{\mathrm{e}}$$. Then $$\mathrm{t}$$ is equal to

A nucleus breaks into two nuclear parts, which have their velocity ratio $$2: 1$$. The ratio of their nuclear radii will be

Ratio centripetal acceleration for an electron revolving in 3^rd and 5^th Bohr orbit of hydrogen atom is

When an electron in hydrogen atom jumps from third excited state to the ground state, the de-Broglie wavelength associated with the electron becomes

'$$\lambda_1$$' is the wavelength of series limit of Lyman series, '$$\lambda_2$$' is the wavelength of the first line line of Lyman series and '$$\lambda_3$$' is the series limit of the Balmer series. Then the relation between $$\lambda_1, \lambda_2$$ and $$\lambda_3$$ is

A sample of radioactive element contains $$8 \times 10^{16}$$ active nuclei. The halt-life of the element is 15 days. The number of nuclei decayed after 60 days is

The P.E. 'U' of a moving particle of mass 'm' varies with 'x'-axis as shown in figure. The deBroglie wavelength or the particle in the regions $$0 \leq x \leq 1$$ and $$x > 1$$ are $$\lambda_1$$ and $$\lambda_2$$ respectively. II the total energy of the particle is '$$\mathrm{nE}$$', then the ratio $$\lambda_1 / \lambda_2$$ is

The gyromagnetic ratio of an electron in an hydrogen atom, according to Bohr model is

The electron in hydrogen atom is initially in the third excited state. When it finally moves to ground state, the maximum number of spectral lines emitted are

If the electron in a hydrogen atom moves from ground state orbit to 5^th orbit, then the potential energy of the electron

The energy levels with transitions for the atom are shown. The transitions corresponding to emission of radiation of maximum and minimum wavelength are respectively

Using Bohr's model, the orbital period of electron in hydrogen atom in $n$th orbit is ( $\varepsilon_0=$ permittivity of free space, $h=$ Planck's constant, $m=$ mass of electron and $\theta=$ electronic charge)

A radioactive nucleus emits $$4 \alpha$$-particles and $$7 \beta$$-particles in succession. The ratio of number of neutrons of that of protons, is [$$A=$$ mass number, $$Z=$$ atomic number]

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) second to first energy level and (ii) highest energy level to second level is respectively

Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ($$I=$$ moment of inertia of diatomic molecule and, $$h=$$ Planck's constant)

The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity of light $$(c)$$ is ( $$h=$$ Planck's constant, $$\varepsilon_0=$$ permittivity of free space, $$e=$$ charge on electron)

The force acting on the electrons in hydrogen atom (Bohr's theory) is related to the principle quantum number $$n$$ as

If the speed of an electron of hydrogen atom in the ground state is $2.2 \times 10^6 \mathrm{~m} / \mathrm{s}$, then its speed in the third excited state will be

In hydrogen emission spectrum, for any series, the principal quantum number is $n$. Corresponding maximum wavelength $\lambda$ is ( $R=$ Rydberg's constant)

When the electron in hydrogen atom jumps from fourth Bohr orbit to second Bohr orbit, one gets the

In Balmer series, wavelength of first line is ' $\lambda_1$ ' and in Brackett series wavelength of first line is ' $\lambda_2$ ' then $\frac{\lambda_1}{\lambda_2}$ is

Bohr model is applied to a particle of mass ' $m$ ' and charge ' $q$ ' is moving in a plane under the influence of a transverse magnetic field ' $B$ '. The energy of the charged particle in the $n$th level will be ( $h=$ Planck's constant)

The angle made by orbital angular momentum of electron with the direction of the orbital magnetic moment is

The wavelength of the first line in Balmer series in the hydrogen spectrum is ' $\lambda$ '. What is the wavelength of the second line in the same series?