Atomic Structure | Physics JEE previous year questions with Solutions

Q 11 :

The radius of $2^{nd}$ orbit of ${He}^{+}$ of Bohr's model is $r_{1}$ and that of fourth orbit of ${Be}^{3 +}$ is represented as $r_{2}$ . Now the ratio $\frac{r_{2}}{r_{1}}$ is $x : 1$ . The value of $x$ is _________ [2023]

(2)

$r \propto \frac{n^{2}}{z}$

$\frac{r_{{He}^{+}}}{r_{{Be}^{3 +}}} = \frac{2^{2} \times 4}{2 \times 4 \times 4} = \frac{1}{2}$

Q 12 :

In hydrogen atom spectrum, $(R \to Rydberg's constant)$

A. the maximum wavelength of the radiation of Lyman series is $\frac{4}{3 R}$
B. the Balmer series lies in the visible region of the spectrum
C. the minimum wavelength of the radiation of Paschen series is $\frac{9}{R}$
D. the minimum wavelength of Lyman series is $\frac{5}{4 R}$

Choose the correct answer from the options given below: [2026]

A, B Only
A, B and C Only
A, B and D Only
B, D Only

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2

3

4

(2)

$\frac{1}{λ} = R (1 - \frac{1}{4})$

$λ = \frac{4}{3 R}$

$\frac{1}{λ'} = R (\frac{1}{9})$

$λ' = \frac{9}{R}$

Q 13 :

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ______ m
(Atomic number of gold = 79 and $\frac{1}{4 π ε_{0}} = 9 \times 10^{9}$ in SI units) [2026]

$3.85 \times 10^{- 16}$
$2.95 \times 10^{- 14}$
$3.85 \times 10^{- 14}$
$2.95 \times 10^{- 16}$

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2

3

4

(2)

Energy conservation

$K_{i} + U_{i} = K_{f} + U_{f}$

$7.7 \times 10^{6} \times 1.6 \times 10^{- 19} + 0$

$= 0 + \frac{9 \times 10^{9} (1.6 \times 10^{- 19}) (79 \times 1.6 \times 10^{- 19})}{r}$

$r = 2.95 \times 10^{- 14}$

Q 14 :

Two electrons are moving in orbits of two hydrogen-like atoms with speeds $3 \times 10^{5} m/s$ and $2.5 \times 10^{5} m/s$ respectively. If the radii of these orbits are nearly same, then the possible order of energy states are _______ respectively. [2026]

8 and 10
6 and 5
10 and 12
9 and 8

1

2

3

4

(2)

$V \propto \frac{Z}{n}$

$r \propto \frac{n^{2}}{Z}$

$Thus, r \propto \frac{n}{V}$

$Radii are same then$

$\frac{n_{1}}{V_{1}} = \frac{n_{2}}{V_{2}}$

$\frac{n_{1}}{n_{2}} = \frac{3 \times 10^{5}}{2.5 \times 10^{5}} = \frac{6}{5}$

$Possible order is 6 and 5$

Q 15 :

7.9 MeV $α$ -particle scatters from a target material of atomic number 79. From the given data, the estimated diameter of nuclei of the target material is (approximately) _____ m.

$[\frac{1}{4 π ε_{0}} = 9 \times 10^{9} {Nm}^{2} / C^{2} and electron charge = 1.6 \times 10^{- 19} C]$ [2026]

$1.44 \times 10^{- 13}$
$2.88 \times 10^{- 14}$
$1.69 \times 10^{- 12}$
$5.76 \times 10^{- 14}$

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2

3

4

(4)

$By mechanical energy conservation$

${(ME)}_{i} = {(ME)}_{f}$

$P E_{i} + K E_{i} = P E_{f} + K E_{f}$

$0 + 7.9 \times 10^{6} \times 1.6 \times 10^{- 19} = \frac{k (2 e) (Z e)}{r} + 0$

$r = \frac{9 \times 10^{9} \times 2 \times {(1.6 \times 10^{- 19})}^{2} \times 79}{7.9 \times 10^{6} \times 1.6 \times 10^{- 19}} = 2.88 \times 10^{- 14} m$

$For diameter \Rightarrow D = 2 r = 5.76 \times 10^{- 14} m$

Q 16 :

The energy of an electron in an orbit of the Bohr’s atom is $- 0.04 E_{0} e V$ where $E_{0}$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck’s constant, then $\frac{2 π L}{h} =$ _____. [2026]

5
2
6
4

1

2

3

4

(1)

$Angular momentum L = \frac{n h}{2 π}$

$n = \frac{2 π L}{h}$

$Energy E = - \frac{13.6}{n^{2}} Z^{2}$

$E \Rightarrow - \frac{E_{0}}{n^{2}} = - 0.04 E_{0}$

$n^{2} = 25, n = 5$

Q 17 :

According to Bohr model, magnetic field at centre (at the nucleus) of a hydrogen atom due to motion of electron in the nth orbit is proportional to

$\frac{1}{n^{3}}$
$\frac{1}{n^{5}}$
$n^{5}$
$n^{3}$

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2

3

4

(2)

$B = \frac{μ_{0} i}{2 r}$ ; magnetic field at centre of hydrogen atom i.e. at nucleus.

$i = \frac{e}{T} = e f \propto \frac{Z^{2}}{n^{3}}$

$r \propto \frac{n^{2}}{Z}$

$B \propto \frac{i}{r} \propto \frac{Z^{3}}{n^{5}}$

$B \propto \frac{1}{n^{5}}$

Q 18 :

The minimum energy of an electron necessary for ionization of an atom of hydrogen, is equal to $W_{0}$ . Suppose that a hydrogen atom and helium atom both in ground state collide inelastically so that hydrogen atom is ionized. If the hydrogen was at rest and helium was moving with at least energy of $x W_{0}$ , find the value of $x$ .

(5)

$Possible loss = \frac{1}{2} \frac{4 m}{5} V^{2} = W_{0}$

$K E_{H e} = \frac{1}{2} 4 m V^{2} = 5 W_{0}$

Q 19 :

Hydrogen gas absorbs radiations of wavelength $λ_{0}$ and consequently emit radiations of 6 different wavelengths of which three wavelengths are shorter than $λ_{0}$ . Choose the CORRECT statement(s).

The final energy state of the atom is $n = 4$
The initial state of the atom may be $n = 2$
There are two transitions in Balmer series
There are three transitions belonging to Lyman series

1

2

3

4

Select one or more options

(1,2,3,4)

Since only 6 different wavelengths are excited, therefore highest excited state is $n = 4$ .

Two wavelengths are shorter than $λ_{0}$ . Initially atoms were in excited state $n = 2$ .

Corresponding transitions are 4 → 3, 4 → 2, 4 → 1, 3 → 2, 3 → 1, 2 → 1.

Q 20 :

An electron in a hydrogen atom makes a transition $n_{1} \to n_{2}$ , where $n_{1}$ and $n_{2}$ are the principal quantum numbers of the two states. Assume Bohr model to be valid.

Column-I Column-II

A) The electron emits an energy of 2.55 eV p) $n_{1} = 2, n_{2} = 1$

B) Time period of the electron in the initial state is eight times that in the final state q) $n_{1} = 4, n_{2} = 2$

C) Speed of electron become two times r) $n_{1} = 5, n_{2} = 3$

D) Radius of orbit of electron becomes 4.77 $A^{0}$ s) $n_{1} = 6, n_{2} = 3$

t) $n_{1} = 8, n_{2} = 4$

A→p, B→p,t, C→p,q,t, D→r
A→p, B→p,t, C→p,q,s,t, D→r
A→q, B→p,q,s,t, C→p,q,s,t, D→r,s
A→r, B→p, C→p,q,s,t, D→q

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4

(3)

$E_{n} = - 13.6 \frac{Z^{2}}{n^{2}} e V, r_{n} = 0.529 \frac{n^{2}}{Z} Å, V_{n} = 2.2 \times 10^{6} \frac{Z}{n} m / s, T = \frac{2 π r_{n}}{v_{n}} .$

Q 21 :

Angular momentum of an electron in a hydrogen atom is $\frac{3 h}{π}$ , then the energy of the electron is ______ eV. [2026]

− 1.51
− 0.85
− 0.38
− 0.28

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3

4

(3)

$L = \frac{n h}{2 π} = \frac{3 h}{π} \Rightarrow n = 6$

$E = \frac{- 13.6}{n^{2}} eV = \frac{- 13.6}{36} eV \approx - 0.38 eV$

Q 22 :

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: [2026]

A, B Only
B, E Only
C, D Only
A, C, E Only

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4

(4)

(A) size of nucleus is small

(C) impact parameter is zero only for few $α$ -particles

(E) only few $α$ -particles can rebound by $180 °$ by head-on collision.

Q 23 :

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 is given by $r_{i} : r_{f} = 16 : 4$ . The wavelength of photon emitted due to this transition is ______ nm. (Given Rydberg constant = $1.0973 \times 10^{7} /m$ ) [2026]

121
242
486
974

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2

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4

(3)

$Given : \frac{r_{i}}{r_{f}} = \frac{16}{4} = \frac{n_{i}^{2}}{n_{f}^{2}}$

$\frac{n_{i}}{n_{f}} = \frac{4}{2}$

$\frac{1}{λ} = R (\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}}) = 1.0973 \times 10^{7} (\frac{1}{{(2)}^{2}} - \frac{1}{{(4)}^{2}})$

$λ = 4.86 \times 10^{- 7} m \approx 486 nm$

Q 24 :

Using Bohr’s model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of hydrogen atom _________. [2026]

(64)

$The magnetic field due to circular loop, B = \frac{μ_{0} I}{2 π r}$

$Current due to orbiting electron, I = \frac{e v}{2 π r}$

$\Rightarrow B \propto \frac{v}{r^{2}}$

$But, v \propto \frac{Z}{n} and r \propto \frac{n^{2}}{Z}$

$\Rightarrow B \propto \frac{(\frac{Z}{n})}{{(\frac{n^{2}}{Z})}^{2}} = \frac{Z^{3}}{n^{5}}$

$\frac{B_{1}}{B_{2}} = \frac{n_{2}^{5}}{n_{1}^{5}} = \frac{4^{5}}{2^{5}} = 64$

Topic Question Set

Q 11 :

The radius of $2^{nd}$ orbit of ${He}^{+}$ of Bohr's model is $r_{1}$ and that of fourth orbit of ${Be}^{3 +}$ is represented as $r_{2}$ . Now the ratio $\frac{r_{2}}{r_{1}}$ is $x : 1$ . The value of $x$ is _________ [2023]

Q 13 :

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ______ m
(Atomic number of gold = 79 and $\frac{1}{4 π ε_{0}} = 9 \times 10^{9}$ in SI units) [2026]

Q 14 :

Two electrons are moving in orbits of two hydrogen-like atoms with speeds $3 \times 10^{5} m/s$ and $2.5 \times 10^{5} m/s$ respectively. If the radii of these orbits are nearly same, then the possible order of energy states are _______ respectively. [2026]

Q 16 :

The energy of an electron in an orbit of the Bohr’s atom is $- 0.04 E_{0} e V$ where $E_{0}$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck’s constant, then $\frac{2 π L}{h} =$ _____. [2026]

Q 17 :

According to Bohr model, magnetic field at centre (at the nucleus) of a hydrogen atom due to motion of electron in the nth orbit is proportional to

Q 19 :

Hydrogen gas absorbs radiations of wavelength $λ_{0}$ and consequently emit radiations of 6 different wavelengths of which three wavelengths are shorter than $λ_{0}$ . Choose the CORRECT statement(s).

Q 21 :

Angular momentum of an electron in a hydrogen atom is $\frac{3 h}{π}$ , then the energy of the electron is ______ eV. [2026]

Q 24 :

Using Bohr’s model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of hydrogen atom _________. [2026]

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	Column-I		Column-II
A)	The electron emits an energy of 2.55 eV	p)	$n_{1} = 2, n_{2} = 1$
B)	Time period of the electron in the initial state is eight times that in the final state	q)	$n_{1} = 4, n_{2} = 2$
C)	Speed of electron become two times	r)	$n_{1} = 5, n_{2} = 3$
D)	Radius of orbit of electron becomes 4.77 $A^{0}$	s)	$n_{1} = 6, n_{2} = 3$
		t)	$n_{1} = 8, n_{2} = 4$

Topic Question Set

Q 11 : The radius of 2nd orbit of He+ of Bohr's model is r1 and that of fourth orbit of Be3+ is represented as r2. Now the ratio r2r1 is x:1. The value of x is _________ [2023]

Q 13 : If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ______ m (Atomic number of gold = 79 and 14πε0=9×109 in SI units) [2026]

Q 14 : Two electrons are moving in orbits of two hydrogen-like atoms with speeds 3×105 m/s and 2.5×105 m/s respectively. If the radii of these orbits are nearly same, then the possible order of energy states are _______ respectively. [2026]

Q 15 : 7.9 MeV α-particle scatters from a target material of atomic number 79. From the given data, the estimated diameter of nuclei of the target material is (approximately) _____ m. [14πε0=9×109 Nm2/C2 and electron charge =1.6×10-19 C] [2026]

Q 16 : The energy of an electron in an orbit of the Bohr’s atom is -0.04E0 eV where E0 is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck’s constant, then 2πLh=_____. [2026]

Q 17 : According to Bohr model, magnetic field at centre (at the nucleus) of a hydrogen atom due to motion of electron in the nth orbit is proportional to

Q 19 : Hydrogen gas absorbs radiations of wavelength λ0 and consequently emit radiations of 6 different wavelengths of which three wavelengths are shorter than λ0. Choose the CORRECT statement(s).

Q 21 : Angular momentum of an electron in a hydrogen atom is 3hπ, then the energy of the electron is ______ eV. [2026]

Q 23 : 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 is given by ri:rf=16:4. The wavelength of photon emitted due to this transition is ______ nm. (Given Rydberg constant = 1.0973×107/m) [2026]

Q 24 : Using Bohr’s model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of hydrogen atom _________. [2026]

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Q 11 :

The radius of $2^{nd}$ orbit of ${He}^{+}$ of Bohr's model is $r_{1}$ and that of fourth orbit of ${Be}^{3 +}$ is represented as $r_{2}$ . Now the ratio $\frac{r_{2}}{r_{1}}$ is $x : 1$ . The value of $x$ is _________ [2023]

Q 13 :

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ______ m
(Atomic number of gold = 79 and $\frac{1}{4 π ε_{0}} = 9 \times 10^{9}$ in SI units) [2026]

Q 14 :

Two electrons are moving in orbits of two hydrogen-like atoms with speeds $3 \times 10^{5} m/s$ and $2.5 \times 10^{5} m/s$ respectively. If the radii of these orbits are nearly same, then the possible order of energy states are _______ respectively. [2026]

Q 16 :

The energy of an electron in an orbit of the Bohr’s atom is $- 0.04 E_{0} e V$ where $E_{0}$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck’s constant, then $\frac{2 π L}{h} =$ _____. [2026]

Q 17 :

According to Bohr model, magnetic field at centre (at the nucleus) of a hydrogen atom due to motion of electron in the nth orbit is proportional to

Q 19 :

Hydrogen gas absorbs radiations of wavelength $λ_{0}$ and consequently emit radiations of 6 different wavelengths of which three wavelengths are shorter than $λ_{0}$ . Choose the CORRECT statement(s).

Q 21 :

Angular momentum of an electron in a hydrogen atom is $\frac{3 h}{π}$ , then the energy of the electron is ______ eV. [2026]

Q 24 :

Using Bohr’s model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of hydrogen atom _________. [2026]