Atoms and Nuclei — JEE Main PYQs

The binding energy per nucleon of $^{209}_{83}\text{Bi}$ is ________ MeV.

[Take $m\left(^{209}_{83}\text{Bi}\right) = 208.980388 \text{ u}$, $m_p = 1.007825 \text{ u}$, $m_n = 1.008665 \text{ u}$, $1 \text{ u} = 931 \text{ MeV/c}^2$]

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{\text{nd}}$ and $4^{\text{th}}$ orbits of hydrogen atom ________.

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass numbers 3, 4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process, $\Delta \mathrm{M}c^2 =$ ______ MeV.

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because

A. The size of gold nucleus is very small as compared to the size of gold atom. B. Alpha particle and gold nucleus have equal charge. C. The impact parameter is minimum for a few alpha particles. D. A few alpha particles have very high kinetic energy. E. Only a few alpha particles undergo head-on collision with the nuclei.

Choose the correct answer from the options given below:

In the hydrogen atom, the electron makes a transition from the higher orbit ($i$) to a lower orbit ($f$). The ratio of the radius of the orbits in given by $r_i : r_f = 16 : 4$. The wavelength of photon emitted due to this transition is ______ nm.

(Given Rydberg constant $= 1.0973 \times 10^7 \text{ /m}$)

Assuming the experimental mass of $^{12}_{6}\text{C}$ as $12 \text{ u}$, the mass defect of $^{12}_{6}\text{C}$ atom is ________ $\text{MeV}/c^2$.

(Mass of proton $= 1.00727 \text{ u}$, mass of neutron $= 1.00866 \text{ u}$, $1 \text{ u} = 931.5 \text{ MeV}/c^2$ and $c$ is the speed of the light in vacuum).

The ratio of momentum of the photons of the $1^{\text{st}}$ and $2^{\text{nd}}$ line of Balmer series of Hydrogen atoms is $\alpha/\beta$. The possible values of $\alpha$ and $\beta$ are:-

The energy released when $\frac{7}{17.13}$ kg of $^{7}_{3}\text{Li}$ is converted into $^{4}_{2}\text{He}$ by proton bombardment is $\alpha \times 10^{32}$ eV. The value of $\alpha$ is ____. (Nearest integer)

(Mass of $^{7}_{3}\text{Li} = 7.0183$ u, mass of $^{4}_{2}\text{He} = 4.004$ u, mass of proton $= 1.008$ u and $1\ \text{u} = 931\ \text{MeV/c}^2$ and Avogadro number $= 6.0 \times 10^{23}$)

The energy released if hydrogen atoms are combined to form $^{4}_{2}\text{He}$ is ________ MeV. (Take binding energies per nucleon of $^{2}_{1}\text{H}$ and $^{4}_{2}\text{He}$ as 1.1 MeV and 7.2 MeV, respectively)

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$-decay with same $Q$ value of $1\,\text{MeV}$. The ratio of energies of $\alpha$-rays produced by A and B is ________.

Considering Bohr's atomic model for hydrogen atom :

(A) the energy of H atom in ground state is same as energy of $\mathrm{He}^+$ ion in its first excited state. (B) the energy of H atom in ground state is same as that for $\mathrm{Li}^{++}$ ion in its second excited state. (C) the energy of H atom in its ground state is same as that of $\mathrm{He}^+$ ion for its ground state. (D) the energy of $\mathrm{He}^+$ ion in its first excited state is same as that for $\mathrm{Li}^{++}$ ion in its ground state.

Choose the correct answer from the options given below :

Energy released when two deuterons $({}_1\mathrm{H}^2)$ fuse to form a helium nucleus $({}_2\mathrm{He}^4)$ is :

(Given : Binding energy per nucleon of ${}_1\mathrm{H}^2 = 1.1$ MeV and binding energy per nucleon of ${}_2\mathrm{He}^4 = 7.0$ MeV)

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $\mathrm{Li}^{++}$ ion in its ground state is given by $\dfrac{1}{\mathrm{X}}\,a_0$, where X = _________.

(Where $a_0$ is the first Bohr's radius.)

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\mathrm{^{1}_{0}n + \, ^{235}_{92}U \to \, ^{140}_{54}Xe + \, ^{94}_{38}Sr + 2\,^{1}_{0}n}$	I.	Chemical reaction
B.	$\mathrm{2H_2 + O_2 \to 2H_2O}$	II.	Fusion with +ve Q value
C.	$\mathrm{^{2}_{1}H + \, ^{2}_{1}H \to \, ^{3}_{2}He + \, ^{1}_{0}n}$	III.	Fission
D.	$\mathrm{^{1}_{1}H + \, ^{3}_{1}H \to \, ^{2}_{1}H + \, ^{2}_{1}H}$	IV.	Fusion with -ve Q value

Choose the correct answer from the options given below:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only.

Reason R : The formulation of Bohr model does not include repulsive force between electrons.

In the light of the above statements, choose the correct answer from the options given below

An electron in the hydrogen atom initially in the fourth excited state makes a transition to $n^{\text{th}}$ energy state by emitting a photon of energy 2.86 eV. The integer value of n will be __________.

A radioactive material P first decays into Q and then Q decays to non-radioactive material R. Which of the following figure represents time dependent mass of P, Q and R ?

[Options are mass vs time graphs]

For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is

In a hydrogen like ion, the energy difference between the 2$^{\text{nd}}$ excitation energy state and ground is 108.8 eV. The atomic number of the ion is:

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The density of the copper $\left(^{64}_{29}\mathrm{Cu}\right)$ nucleus is greater than that of the carbon $\left(^{12}_{6}\mathrm{C}\right)$ nucleus.

Reason (R) : The nucleus of mass number A has a radius proportional to $A^{1/3}$.

In the light of the above statements, choose the most appropriate answer from the options given below :

For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as

In the lowest state of a hydrogen atom, the orbital radius of an electron is $5.3 \times 10^{-11}$ m, while in the third excited state the orbital radius of the same electron is $8.48 \times 10^{-10}$ m. The ratio of the de-Broglie wavelengths of the electron in the excited state with that in the lowest state is :

The decay constant of a radioactive nucleus $\mathrm{n_2}$ is 3 times that of another radioactive nucleus $\mathrm{n_1}$. If the initial number of both nuclei is the same, what is the ratio of the number of nuclei of $\mathrm{n_2}$ to the number of nuclei of $\mathrm{n_1}$ after one half-life of $\mathrm{n_1}$?

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A, for nuclei with mass numbers between 30 and 170.

Reason (R) : Nuclear force is long range.

In the light of the above statements, choose the correct answer from the options given below :

During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is 2000 Å and it becomes 6000 Å when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is

Choose the correct nuclear process from the below options

[p: proton, n: neutron, $e^-$: electron, $e^+$: positron, $\nu$: neutrino, $\bar{\nu}$: antineutrino]

The frequency of revolution of the electron in Bohr's orbit varies with n, where n is the principal quantum number, as :

Which of the following nuclear fragments corresponding to nuclear fission between neutron $\left({}^{1}_{0}\mathrm{n}\right)$ and uranium isotope $\left({}^{235}_{92}\mathrm{U}\right)$ is correct :

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 $1 \times 10^{-n}$. The value of n is ________.

[Given Rhc = 13.6 eV, hc = 1242 eV nm, h = $6.6 \times 10^{-34}$ J s mass of the hydrogenatom = $1.6 \times 10^{-27}$ kg]

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

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

Given atomic masses of $^{235}U$: $235.0439\,u$; $^{140}Ce$ : $139.9054\,u$,

$^{94}Zr$ : $93.9063\,u$ ; $n$ : $1.0086\,u$,

Value of $c^2 = 931~MeV/u$.

An electron rotates in a circle around a nucleus having positive charge Ze. Correct relation between total energy (E) of electron to its potential energy (U) is :

If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is ________ $\times 10^{-2}$ MeV. (Given $1\ \mathrm{u} = 931\ \mathrm{MeV/c^2}$, atomic mass of helium $= 4.002603\mathrm{u}$)

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

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $915\ \mathrm{\mathring{A}}$. The longest wavelength of spectral lines in the Balmer series will be ________ $\mathrm{\mathring{A}}$.

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

Radius of a certain orbit of hydrogen atom is 8.48 Å. If energy of electron in this orbit is $E/x$, then $x =$ _________.

(Given $\mathrm{a}_o = 0.529$ Å, $E$ = energy of electron in ground state).

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

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ________ nm. (Given $hc = 1245\ \mathrm{eV\,nm}$, $e = 1.6 \times 10^{-19}\ \mathrm{C}$).

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

In an alpha particle scattering experiment distance of closest approach for the $\alpha$ particle is $4.5 \times 10^{-14}$ m. If target nucleus has atomic number 80, then maximum velocity of $\alpha$-particle is___________ $\times 10^{5}$ m/s approximately.

($\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ SI unit, mass of $\alpha$ particle $= 6.72 \times 10^{-27}$ kg)

If $\mathrm{M_o}$ is the mass of isotope $\mathrm{^{12}_{5}B}$, $\mathrm{M_p}$ and $\mathrm{M_n}$ are the masses of proton and neutron, then nuclear binding energy of isotope is :

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

The energy equivalent of 1 g of substance is :

A star has 100% helium composition. It starts to convert three $^{4}\mathrm{He}$ into one $^{12}\mathrm{C}$ via triple alpha process as $^{4}\mathrm{He} + {}^{4}\mathrm{He} + {}^{4}\mathrm{He} \rightarrow {}^{12}\mathrm{C} + Q$. The mass of the star is $2.0 \times 10^{32}$ kg and it generates energy at the rate of $5.808 \times 10^{30}$ W. The rate of converting these $^{4}\mathrm{He}$ to $^{12}\mathrm{C}$ is $n \times 10^{42}\ \mathrm{s^{-1}}$, where n is ________.

[ Take, mass of $^{4}\mathrm{He} = 4.0026$ u, mass of $^{12}\mathrm{C} = 12$ u]

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

The energy released in the fusion of 2 kg of hydrogen deep in the sun is $E_H$ and the energy released in the fission of 2 kg of $^{235}\mathrm{U}$ is $E_U$. The ratio $\frac{E_H}{E_U}$ is approximately:

(Consider the fusion reaction as $4{}^{1}_{1}\mathrm{H} + 2e^- \rightarrow {}^{4}_{2}He + 2\nu + 6\gamma + 26.7$ MeV, energy released in the fission reaction of $^{235}\mathrm{U}$ is 200 $MeV$ per fission nucleus and $\mathrm{N_A} = 6.023\times10^{23}$)

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

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 $\dfrac{1000}{x}$, where $x$ is ________.

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 forces do not obey inverse square law. (C) Nuclear forces are spin dependent. (D) Nuclear forces are central and charge independent. (E) Stability of nucleus is inversely proportional to the value of packing fraction.

Choose the correct answer from the options given below :

A particular hydrogen - like ion emits the radiation of frequency $3 \times 10^{15}$ Hz when it makes transition from n = 2 to n = 1. The frequency of radiation emitted in transition from n = 3 to n = 1 is $\frac{x}{9} \times 10^{15}$ Hz, when $x =$ ________.

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

In a nuclear fission process, a high mass nuclide $(A \approx 236)$ with binding energy 7.6 MeV/Nucleon dissociated into middle mass nuclides $(A \approx 118)$, having binding energy of 8.6 MeV/Nucleon. The energy released in the process would be ________ MeV.

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 chain reaction is given by

$$_3\mathrm{Li}^6 + {_0\mathrm{n}^1} \rightarrow {_2\mathrm{He}^4} + {_1\mathrm{H}^3}$$

$$_1\mathrm{H}^2 + {_1\mathrm{H}^3} \rightarrow {_2\mathrm{He}^4} + {_0\mathrm{n}^1}$$

During the explosion the energy released is approximately

[Given ; M (Li) = 6.01690 amu, M ($_1\mathrm{H}^2$) = 2.01471 amu, M ($_2\mathrm{He}^4$) = 4.00388 amu, and 1 amu = 931.5 MeV]

When a hydrogen atom going from $n=2$ to $n=1$ emits a photon, its recoil speed is $\frac{x}{5}\ m/s$. Where $x =$ ________. (Use, mass of hydrogen atom $= 1.6 \times 10^{-27}$ kg)

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the $5^{\text{th}}$ excited state of a hydrogen atom is :

A electron of hydrogen atom on an excited state is having energy $\mathrm{E_n} = -0.85~\mathrm{eV}$. The maximum number of allowed transitions to lower energy level 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 terms of mass defect $\Delta M$ 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

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

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

(speed of light $= 3 \times 10^8$ m/s)

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

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 $A_2 = 4A_1$, then $\frac{V_2}{V_1} =$ ________.