Atomic Structure | Physics JEE previous year questions with Solutions

Q 1 :

According to Bohr's theory, the moment of momentum of an electron revolving in 4th orbit of hydrogen atom is [2024]

$\frac{h}{2 π}$
$8 \frac{h}{π}$
$2 \frac{h}{π}$
$\frac{h}{π}$

1

2

3

4

(3)

Moment of momentum or angular momentum, $L = \frac{n h}{2 π}$

put $n = 4$

$L = \frac{4 h}{2 π} = \frac{2 h}{π}$

Q 2 :

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 [2024]

2E = 3U
E = 2U
E = U
2E = U

1

2

3

4

(4)

Total energy $E = \frac{- k Z e^{2}}{2 r}$

Potential energy $U = \frac{- k Z e^{2}}{r} \Rightarrow U = 2 E$

Q 3 :

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of [2024]

$10^{39}$
$10^{19}$
$10^{29}$
$10^{36}$

1

2

3

4

(1)

$F_{e} = \frac{k Q_{1} Q_{2}}{r^{2}} = \frac{9 \times 10^{9} \times 1.6 \times 10^{- 19} \times 1.6 \times 10^{- 19}}{r^{2}}$

$F_{g} = \frac{G m_{1} m_{2}}{r^{2}} = \frac{6.67 \times 10^{- 11} \times 9.1 \times 10^{- 31} \times 1.6 \times 10^{- 27}}{r^{2}}$

$\frac{F_{e}}{F_{g}} ≅ 0.23 \times 10^{40} ≅ 2.3 \times 10^{39}$

Q 4 :

The angular momentum of an electron in a hydrogen atom is proportional to

(Where r is the radius of orbit of electron) [2024]

$\frac{1}{r}$
$r$
$\sqrt{r}$
$\frac{1}{\sqrt{r}}$

1

2

3

4

(3)

The radius of $n^{t h}$ orbit is, $r \propto \frac{n^{2}}{Z}, \Rightarrow n \propto \sqrt{Z r}$ ...(i)

where, Z is atomic number.

Angular momentum is given by, $L = \frac{n h}{2 π}$ ...(ii)

Put value of $n$ from (i) to equation (ii),

$L = \frac{\sqrt{Z r} h}{2 π} = (\frac{\sqrt{Z} h}{2 π}) \sqrt{r} \Rightarrow L \propto \sqrt{r}$

Q 5 :

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? [2024]

6
3
10
1

1

2

3

4

(4)

$As, E_{n} \propto \frac{Z^{2}}{n^{2}}$

$Energy of the 2 nd orbit E_{2} = \frac{- 13.6}{4} = - 3.4 eV$

$Δ E_{2 \to 1} = 10.2 eV$

$So, only possible transition is from n = 2 to n = 1$

Q 6 :

The radius of third stationary orbit of electron for Bohr's atom is P. The radius of fourth stationary orbit will be [2024]

$\frac{4}{3} R$
$\frac{16}{9} R$
$\frac{3}{4} R$
$\frac{9}{16} R$

1

2

3

4

(2)

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

$\frac{r_{4}}{r_{3}} = \frac{4^{2}}{3^{2}} \Rightarrow r_{4} = \frac{16}{9} R$

Q 7 :

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 electrons revolve around it, is Rutherford's model.

Statement II: An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model.

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

Statement I is true but Statement II is false
Both Statement I and Statement II are true
Both statement I and statement II are false
Statement I is false but Statement II is true

1

2

3

4

(1)

According to Rutherford atomic model, most of mass of atom and all its positive charge is concentrated in tiny nucleus and electron revolve around it.

According to Thomson atomic model, atom is spherical cloud of positive charge with electron embedded in it.

Hence, Statement I is true but statement II is false.

Q 8 :

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: [2024]

4
1/4
1/2
1

1

2

3

4

(3)

In Bohr's model, for a given state or orbit

$K E = - \frac{P E}{2}$ or $| K E | = \frac{| P E |}{2}$

therefore, $\frac{| K E |}{| P E |} = \frac{1}{2}$

Q 9 :

An electron revolving in $n^{t h}$ Bohr orbit has magnetic moment $μ_{n} .$ If $μ_{n}$ $α$ $n^{x}$ , the value of $x$ is [2024]

2
1
3
0

1

2

3

4

(2)

$Magnetic moment (m) = I A$

$= \frac{e}{T} \cdot π r^{2} = \frac{e}{(\frac{2 π r}{v})} \cdot π r^{2} = \frac{e r v}{2}$

$We know that r \propto n^{2} and v \propto \frac{1}{n}$

$S o μ \propto r v$

$μ \propto \frac{n^{2}}{n} \Rightarrow μ \propto n = 1$

Q 10 :

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 $a_{0}$ = 0.529 $Å$ , E = energy of electron in ground state). [2024]

(16) $We know, r = r_{0} \cdot \frac{n^{2}}{Z} = 0.529 \frac{n^{2}}{Z}$

$For hydrogen, Z = 1$

$8.48 = 0.529 n^{2}; n^{2} = 16; n = 4$

$Energy of electron in n^{t h} orbit {(E)}^{'} = \frac{E}{n^{2}} = \frac{E}{16} \Rightarrow x = 16$

Q 11 :

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

$(\frac{1}{4 π ε_{0}} = 9 \times 10^{9}$ SI unit, mass of $α$ particle = $6.72 \times 10^{- 27}$ kg $)$ [2024]

(156) $\frac{K Q q}{r_{\min}} = \frac{1}{2} m v^{2} \Rightarrow v = \sqrt{\frac{2 K (Z e) \cdot (2 e) q}{m r_{\min}}} = \sqrt{\frac{4 K Z e^{2}}{m r_{\min}}}$

$\Rightarrow v = \sqrt{\frac{4 \times 9 \times 10^{9} \times 80 \times {(1.6 \times 10^{- 19})}^{2}}{6.72 \times 10^{- 27} \times 4.5 \times 10^{- 14}}}$

$= 1.56 \times 10^{7} m / s = 156 \times 10^{5} m / s$

Q 12 :

If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be $\frac{α}{7 R}$ , where $α$ = _______ . [2024]

(144) Longest wavelength corresponds to transition between $n = 3$ and $n = 4$

$\frac{1}{λ} = R Z^{2} (\frac{1}{3^{2}} - \frac{1}{4^{2}}) = R Z^{2} (\frac{1}{9} - \frac{1}{16}) = \frac{7 R Z^{2}}{9 \times 16}$

$\Rightarrow λ = \frac{144}{7 R}$ for $Z = 1$

$∴ α = 144$

Q 13 :

A electron of hydrogen atom in an excited state is having energy $E_{n} = - 0.85$ $e V$ . The maximum number of allowed transitions to lower energy level is ______ . [2024]

(6) $E_{n} = - \frac{13.6}{n^{2}} = - 0.85 \Rightarrow n = 4$

$Number of transitions = \frac{n (n - 1)}{2} = \frac{4 (4 - 1)}{2} = 6$

Q 14 :

A hydrogen atom changes its state from $n = 3 t o n = 2$ . Due to recoil, the percentage change in the wavelength of emitted light is approximately $1 \times 10^{- n}$ . The value of n is ____.

[Given $R h c = 13.6 eV, h c = 1242 eVnm, h = 6.6 \times 10^{- 34}$ mass of the hydrogen atom = $1.6 \times 10^{- 27} kg$ ] [2024]

(7)

For $n = 3$ to $n = 2$

$Δ E = 13.6 (\frac{1}{2^{2}} - \frac{1}{3^{2}}) = 1.9 eV$

$Δ E = \frac{h c}{λ} \Rightarrow λ = \frac{h c}{Δ E}$

If recoil takes place

$P_{i} = P_{f} \Rightarrow 0 = - m v + \frac{h}{λ'} \Rightarrow v = \frac{h}{m λ'}$

$Δ E = \frac{1}{2} m v^{2} + \frac{h c}{λ'} = \frac{1}{2} m {(\frac{h}{m λ'})}^{2} + \frac{h c}{λ'}$

Now, $Δ E = \frac{h^{2}}{2 m λ'^{2}} + \frac{h c}{λ'}$

$λ'^{2} Δ E - h c λ' - \frac{h^{2}}{2 m} = 0$

$λ' = \frac{h c \pm \sqrt{h^{2} c^{2} + \frac{4 Δ E h^{2}}{2 m}}}{2 Δ E}$

$λ' = \frac{h c \pm h c \sqrt{1 + \frac{2 Δ E}{m c^{2}}}}{2 Δ E}$

$\frac{λ'}{λ} = \frac{1 + {(1 + \frac{2 Δ E}{m c^{2}})}^{\frac{1}{2}}}{2} = \frac{1 + 1 + \frac{Δ E}{m c^{2}}}{2}$

$\frac{λ'}{λ} = 1 + \frac{Δ E}{2 m c^{2}}$

$\frac{λ' - λ}{λ} = \frac{Δ E}{2 m c^{2}} = \frac{1.9 \times 1.6 \times 10^{- 19}}{2 \times 1.67 \times 10^{- 27} \times 9 \times 10^{16}} = 10^{- 9}$

$∴$ $% change \approx 10^{- 7}$

Q 15 :

When a hydrogen atom going from $n = 2 to n = 1$ emits a photon, its recoil speed is $x / 5$ m/s. Where $x =$ ______.

(Use: mass of hydrogen atom = $1.6 \times 10^{- 27} kg$ ) [2024]

(17)

The hydrogen atom transitions from $n = 2$ to $n = 1,$

$Δ E = - 10.2 eV$

Recoil speed $v = \frac{Δ E}{m c}$

$= \frac{10.2 eV}{1.6 \times 10^{- 27} \times 3 \times 10^{8}} = \frac{10.2 \times 1.6 \times 10^{- 19}}{1.6 \times 10^{- 27} \times 3 \times 10^{8}}$

$v = 3.4 m/s = \frac{17}{5} m/s$

Therefore, $x = 17$

Q 16 :

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr quantization is applicable, then the radius of the electronic orbit in the first excited state is: [2025]

$\sqrt{\frac{2 h}{π e B}}$
$\sqrt{\frac{4 h}{π e B}}$
$\sqrt{\frac{h}{2 π e B}}$
$\sqrt{\frac{h}{π e B}}$

1

2

3

4

(4)

$m v r = \frac{n h}{2 π}$ ...(i)

$r = \frac{v m}{B q}$ ...(ii)

n = 2

$m r (\frac{r B q}{m}) = \frac{2 h}{2 π} \Rightarrow r = \sqrt{\frac{h}{π B q}}$

$q = e \Rightarrow r = \sqrt{\frac{h}{π B e}}$

Q 17 :

The frequency of revolution of the electron in Bohr's orbit varies with n, the principal quantum number as [2025]

$\frac{1}{n}$
$\frac{1}{n^{3}}$
$\frac{1}{n^{4}}$
$\frac{1}{n^{2}}$

1

2

3

4

(2)

$f = \frac{v}{2 π r} = (\frac{v_{0}}{n}) (\frac{1}{2 π r_{0} n^{2}})$

$f = \frac{v_{0}}{2 π r_{0}} (\frac{1}{n^{3}}) = f_{0} (\frac{1}{n^{3}})$

Q 18 :

Considering Bohr's atomic model for hydrogen atom:

(A) the energy of H atom in ground state is same as energy of ${He}^{+}$ ion in its first excited state.

(B) the energy of H atom in ground state is same as that for ${Li}^{+ +}$ ion in its second excited state.

(C) the energy of H atom in its ground state is same as that of ${He}^{+}$ ion for its ground state.

(D) the energy of ${He}^{+}$ ion in its first excited state is same as that for ${Li}^{+ +}$ ion in its ground state.

Choose the correct answer from the options given below: [2025]

(B), (D) only
(A), (B) only
(A), (D) only
(A), (C) only

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2

3

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(2)

$E = - 13.6 \frac{z_{2}}{n^{2}} eV$

$E_{{He}^{+}} 1^{st}$ excited state = –13.6 eV

$E_{{Li}^{2 +}} 2^{nd}$ excited state = –13.6 eV

(A), (B) are correct.

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

$Z_{H} = 1 Z_{{He}^{+}} = 2 Z_{{Li}^{+ 2}} = 3$

$1^{st}$ excited state $\Rightarrow$ n = 2

$2^{nd}$ excited state $\Rightarrow$ n = 3

From the given statements only (A) and (B) are correct.

Q 19 :

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of ${Li}^{+ +}$ ion in its ground state is given by $\frac{1}{X} a_{0}$ , where X =. (Where $a_{0}$ is the first Bohr's radius.) [2025]

2
1
3
9

1

2

3

4

(3)

$r = a_{0} \frac{n^{2}}{Z} and Z = 3 for {Li}^{+ 2} and n = 1$

$∴ r = a_{0} \frac{1^{2}}{3} = \frac{a_{0}}{3}$

$∴ X = 3$

Q 20 :

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: [2025]

Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
(A) is false but R is true.
Both (A) and (R) are true and (R) is the correct explanation of (A).
(A) is true but (R) is false.

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2

3

4

(3)

Assertion is correct, Reason is correct as there are no two electrons for repulsion.

Therefore (3) is most appropriate response

Q 21 :

Consider the Bohr model of hydrogen like atoms, the ratio of the radius of $5^{th}$ orbit of the electron in ${Li}^{2 +}$ and ${He}^{+}$ is [2025]

$\frac{3}{2}$
$\frac{4}{9}$
$\frac{9}{4}$
$\frac{2}{3}$

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2

3

4

(4)

$r = a_{0} \cdot \frac{n^{2}}{Z}$

For ${Li}^{2 +}$ : $r_{5} = a_{0} \cdot \frac{25}{3}$

for ${He}^{+}$ : $r_{5} = a_{0} \cdot \frac{25}{2}$

$∴ \frac{r_{{Li}^{2 +}}}{r_{{He}^{+}}} = \frac{2}{3}$

Q 22 :

Given below are two statements:

Statement (I) : The dimensions of Planck's constant and angular momentum are same.

Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant.

In the light of the above statements, choose the most appropriate answer from the options given below: [2025]

Both Statement I and Statement II are correct.
Statement I is incorrect but Statement II is correct.
Statement I is correct but Statement II is incorrect.
Both Statement I and Statement II are incorrect.

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2

3

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(3)

E = hf

$M L^{2} T^{- 2} = [h] \times [T^{- 1}]$

$[h] = [M L^{2} T^{- 1}]$

$L = [M V R] = [M L^{2} T^{- 1}]$

$L = \frac{n h}{2 π}$

L is integral multiple of $\frac{h}{2 π}$

Q 23 :

In a hydrogen like ion, the energy difference between the $2^{nd}$ excitation energy state and ground is 108.8 eV. The atomic number of the ion is [2025]

4
2
1
3

1

2

3

4

(4)

$△ E = 13.6 Z^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$

$13.6 Z^{2} [\frac{1}{1} - \frac{1}{9}] = 108.8$

$\frac{13.6 \times 8}{9} (Z^{2}) = 108.8 \Rightarrow Z = 3$

Q 24 :

An electron in the hydrogen atom initially in the fourth excited state makes a transition to n energy state by emitting a photon of energy 2.86 eV. The integer value of n will be ________. [2025]

(2)

$E = 13.6 (\frac{1}{n_{1}^{2}} - \frac{1}{n_{1}^{2}})$

$2.86 = 13.6 (\frac{1}{n^{2}} - \frac{1}{5^{2}})$

$\frac{1}{n^{2}} = 0.21 + \frac{1}{25}$

$n^{2} = 4 \Rightarrow n = 2$

Q 25 :

A photon is emitted in transition from $n = 4$ to $n = 1$ level in hydrogen atom. The corresponding wavelength for this transition is (given, $h = 4 \times 10^{- 15}$ eV s) [2023]

941 nm
974 nm
99.3 nm
94.1 nm

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2

3

4

(4)

$\frac{h c}{λ} = + 13.6 eV [\frac{1}{1} - \frac{1}{4^{2}}]$

$\Rightarrow \frac{4 \times 10^{- 15} \times 3 \times 10^{- 8}}{λ} = 13.6 [\frac{15}{16}]$

$So, λ = 94.1 nm$

Q 26 :

Speed of an electron in Bohr's $7^{th}$ orbit for Hydrogen atom is $3.6 \times 10^{6} m/s.$ The corresponding speed of the electron in $3^{rd}$ orbit, in m/s is [2023]

$1.8 \times 10^{6}$
$7.5 \times 10^{6}$
$3.6 \times 10^{6}$
$8.4 \times 10^{6}$

1

2

3

4

(4)

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

$z = 1$

$∴$ $V_{n} \propto \frac{1}{n}$

$∴$ $\frac{V_{3}}{V_{7}} = \frac{7}{3}$

$∴$ $V_{3} = \frac{7}{3} V_{7} = \frac{7}{3} \times 3.6 \times 10^{6} m/s = 8.4 \times 10^{6} m/s$

Q 27 :

The radius of electron’s second stationary orbit in Bohr’s atom is R. The radius of 3rd orbit will be [2023]

$\frac{R}{3}$
$2.25 R$
$3 R$
$9 R$

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2

3

4

(2)

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

$\frac{r_{2 nd}}{r_{3 rd}} = {(\frac{n_{2}}{n_{3}})}^{2}$

$\Rightarrow \frac{R}{r_{3 rd}} = {(\frac{2}{3})}^{2}$

$\Rightarrow r_{3 rd} = \frac{9}{4} R = 2.25 R$

Q 28 :

A small particle of mass $m$ moves in such a way that its potential energy $U = \frac{1}{2} m ω^{2} r^{2}$ where $ω$ is constant and $r$ is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of $n^{th}$ orbit will be proportional to. [2023]

$\sqrt{n}$
$n$
$n^{2}$
$\frac{1}{n}$

1

2

3

4

(1)

$U = \frac{1}{2} m ω^{2} r^{2}$

$F = - \frac{d U}{d r} = - m ω^{2} r$

$Now m ω^{2} r = \frac{m v^{2}}{r} \Rightarrow v = ω r \dots (i)$

$and m v r = \frac{n h}{2 π} \dots (i i)$

$From (i) and (ii),$

$m ω r^{2} = \frac{n h}{2 π} \Rightarrow r \propto \sqrt{n}$

Q 29 :

A light of energy 12.75 eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $\frac{x}{π} \times 10^{- 17} eV s$ . The value of $x$ is _________

(use $h = 4.14 \times 10^{- 15} eVs, c = 3 \times 10^{8} {ms}^{- 1}$ ) [2023]

(828)

$In the ground state energy = - 13.6 eV$

$So energy \frac{- 13.6 eV}{n^{2}} = - 13.6 + 12.75$

$\frac{- 13.6 eV}{n^{2}} = - 0.85$

$n = \sqrt{16} = 4$

$Angular momentum = \frac{n h}{2 π} = \frac{4 h}{2 π} = \frac{2 h}{π}$

$Angular momentum = \frac{2}{π} \times 4.14 \times 10^{- 15}$ $= \frac{828 \times 10^{- 17}}{π} eVs$

Q 30 :

Experimentally it is found that 12.8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is $\frac{9}{x} \times 10^{- 10} m$ . The value of the $x$ is _________.

$(1 eV = 1.6 \times 10^{- 19} J, \frac{1}{4 π ε_{0}} = 9 \times 10^{9} {Nm}^{2} / C^{2}$ and electronic charge $= 1.6 \times 10^{- 19} J C)$ [2023]

(16)

$Binding energy of system = \frac{k e^{2}}{2 r} joule and \frac{k e^{2}}{2 r} = 12.8 eV$

$\frac{9 \times 10^{9} \times {(1.6 \times 10^{- 19})}^{2}}{2 r} = 12.8 \times 1.6 \times 10^{- 19}$

$\Rightarrow r = \frac{9 \times 10^{9} \times 1.6 \times 10^{- 19}}{12.8 \times 2}$

$\Rightarrow r = \frac{9 \times 10^{- 10}}{16}$

Topic Question Set

Q 1 :

According to Bohr's theory, the moment of momentum of an electron revolving in 4th orbit of hydrogen atom is [2024]

Q 2 :

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 [2024]

Q 3 :

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of [2024]

Q 4 :

The angular momentum of an electron in a hydrogen atom is proportional to

(Where r is the radius of orbit of electron) [2024]

Q 5 :

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? [2024]

Q 6 :

The radius of third stationary orbit of electron for Bohr's atom is P. The radius of fourth stationary orbit will be [2024]

Q 8 :

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: [2024]

Q 9 :

An electron revolving in $n^{t h}$ Bohr orbit has magnetic moment $μ_{n} .$ If $μ_{n}$ $α$ $n^{x}$ , the value of $x$ is [2024]

Q 10 :

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 $a_{0}$ = 0.529 $Å$ , E = energy of electron in ground state). [2024]

Q 12 :

If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be $\frac{α}{7 R}$ , where $α$ = _______ . [2024]

Q 13 :

A electron of hydrogen atom in an excited state is having energy $E_{n} = - 0.85$ $e V$ . The maximum number of allowed transitions to lower energy level is ______ . [2024]

Q 15 :

When a hydrogen atom going from $n = 2 to n = 1$ emits a photon, its recoil speed is $x / 5$ m/s. Where $x =$ ______.

(Use: mass of hydrogen atom = $1.6 \times 10^{- 27} kg$ ) [2024]

Q 16 :

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr quantization is applicable, then the radius of the electronic orbit in the first excited state is: [2025]

Q 17 :

The frequency of revolution of the electron in Bohr's orbit varies with n, the principal quantum number as [2025]

Q 19 :

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of ${Li}^{+ +}$ ion in its ground state is given by $\frac{1}{X} a_{0}$ , where X =. (Where $a_{0}$ is the first Bohr's radius.) [2025]

Q 21 :

Consider the Bohr model of hydrogen like atoms, the ratio of the radius of $5^{th}$ orbit of the electron in ${Li}^{2 +}$ and ${He}^{+}$ is [2025]

Q 23 :

In a hydrogen like ion, the energy difference between the $2^{nd}$ excitation energy state and ground is 108.8 eV. The atomic number of the ion is [2025]

Q 24 :

An electron in the hydrogen atom initially in the fourth excited state makes a transition to n energy state by emitting a photon of energy 2.86 eV. The integer value of n will be ________. [2025]

Q 25 :

A photon is emitted in transition from $n = 4$ to $n = 1$ level in hydrogen atom. The corresponding wavelength for this transition is (given, $h = 4 \times 10^{- 15}$ eV s) [2023]

Q 26 :

Speed of an electron in Bohr's $7^{th}$ orbit for Hydrogen atom is $3.6 \times 10^{6} m/s.$ The corresponding speed of the electron in $3^{rd}$ orbit, in m/s is [2023]

Q 27 :

The radius of electron’s second stationary orbit in Bohr’s atom is R. The radius of 3rd orbit will be [2023]

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Topic Question Set

Q 1 : According to Bohr's theory, the moment of momentum of an electron revolving in 4th orbit of hydrogen atom is [2024]

Q 2 : 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 [2024]

Q 3 : In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of [2024]

Q 4 : The angular momentum of an electron in a hydrogen atom is proportional to (Where r is the radius of orbit of electron) [2024]

Q 5 : 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? [2024]

Q 6 : The radius of third stationary orbit of electron for Bohr's atom is P. The radius of fourth stationary orbit will be [2024]

Q 8 : 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: [2024]

Q 9 : An electron revolving in nth Bohr orbit has magnetic moment μn. If μn α nx, the value of x is [2024]

Q 10 : 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 a0 = 0.529 Å, E = energy of electron in ground state). [2024]

Q 11 : In an alpha particle scattering experiment distance of closest approach for the α particle is 4.5×10-14m. If target nucleus has atomic number 80, then maximum velocity of α-particle is ________ ×105m/s approximately. (14πε0=9×109 SI unit, mass of α particle = 6.72×10-27 kg) [2024]

Q 12 : If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be α7R, where α = _______ . [2024]

Q 13 : A electron of hydrogen atom in an excited state is having energy En=-0.85 eV. The maximum number of allowed transitions to lower energy level is ______ . [2024]

Q 14 : A hydrogen atom changes its state from n=3 to n=2. Due to recoil, the percentage change in the wavelength of emitted light is approximately 1×10-n. The value of n is ____. [Given Rhc=13.6 eV, hc=1242 eVnm, h=6.6×10-34 mass of the hydrogen atom = 1.6×10-27 kg] [2024]

Q 15 : When a hydrogen atom going from n=2 to n=1 emits a photon, its recoil speed is x/5 m/s. Where x= ______. (Use: mass of hydrogen atom = 1.6×10-27kg) [2024]

Q 16 : An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr quantization is applicable, then the radius of the electronic orbit in the first excited state is: [2025]

Q 17 : The frequency of revolution of the electron in Bohr's orbit varies with n, the principal quantum number as [2025]

Q 19 : Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of Li++ ion in its ground state is given by 1Xa0, where X =. (Where a0 is the first Bohr's radius.) [2025]

Q 21 : Consider the Bohr model of hydrogen like atoms, the ratio of the radius of 5th orbit of the electron in Li2+ and He+ is [2025]

Q 23 : In a hydrogen like ion, the energy difference between the 2nd excitation energy state and ground is 108.8 eV. The atomic number of the ion is [2025]

Q 24 : An electron in the hydrogen atom initially in the fourth excited state makes a transition to n energy state by emitting a photon of energy 2.86 eV. The integer value of n will be ________. [2025]

Q 25 : 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=4×10-15 eV s) [2023]

Q 26 : Speed of an electron in Bohr's 7th orbit for Hydrogen atom is 3.6×106 m/s. The corresponding speed of the electron in 3rd orbit, in m/s is [2023]

Q 27 : The radius of electron’s second stationary orbit in Bohr’s atom is R. The radius of 3rd orbit will be [2023]

Q 28 : A small particle of mass m moves in such a way that its potential energy U=12mω2r2 where ω is constant and r is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of nth orbit will be proportional to. [2023]

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Q 1 :

According to Bohr's theory, the moment of momentum of an electron revolving in 4th orbit of hydrogen atom is [2024]

Q 2 :

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 [2024]

Q 3 :

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of [2024]

Q 4 :

The angular momentum of an electron in a hydrogen atom is proportional to

(Where r is the radius of orbit of electron) [2024]

Q 5 :

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? [2024]

Q 6 :

The radius of third stationary orbit of electron for Bohr's atom is P. The radius of fourth stationary orbit will be [2024]

Q 8 :

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: [2024]

Q 9 :

An electron revolving in $n^{t h}$ Bohr orbit has magnetic moment $μ_{n} .$ If $μ_{n}$ $α$ $n^{x}$ , the value of $x$ is [2024]

Q 10 :

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 $a_{0}$ = 0.529 $Å$ , E = energy of electron in ground state). [2024]

Q 12 :

If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be $\frac{α}{7 R}$ , where $α$ = _______ . [2024]

Q 13 :

A electron of hydrogen atom in an excited state is having energy $E_{n} = - 0.85$ $e V$ . The maximum number of allowed transitions to lower energy level is ______ . [2024]

Q 15 :

When a hydrogen atom going from $n = 2 to n = 1$ emits a photon, its recoil speed is $x / 5$ m/s. Where $x =$ ______.

(Use: mass of hydrogen atom = $1.6 \times 10^{- 27} kg$ ) [2024]

Q 16 :

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr quantization is applicable, then the radius of the electronic orbit in the first excited state is: [2025]

Q 17 :

The frequency of revolution of the electron in Bohr's orbit varies with n, the principal quantum number as [2025]

Q 19 :

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of ${Li}^{+ +}$ ion in its ground state is given by $\frac{1}{X} a_{0}$ , where X =. (Where $a_{0}$ is the first Bohr's radius.) [2025]

Q 21 :

Consider the Bohr model of hydrogen like atoms, the ratio of the radius of $5^{th}$ orbit of the electron in ${Li}^{2 +}$ and ${He}^{+}$ is [2025]

Q 23 :

In a hydrogen like ion, the energy difference between the $2^{nd}$ excitation energy state and ground is 108.8 eV. The atomic number of the ion is [2025]

Q 24 :

An electron in the hydrogen atom initially in the fourth excited state makes a transition to n energy state by emitting a photon of energy 2.86 eV. The integer value of n will be ________. [2025]

Q 25 :

A photon is emitted in transition from $n = 4$ to $n = 1$ level in hydrogen atom. The corresponding wavelength for this transition is (given, $h = 4 \times 10^{- 15}$ eV s) [2023]

Q 26 :

Speed of an electron in Bohr's $7^{th}$ orbit for Hydrogen atom is $3.6 \times 10^{6} m/s.$ The corresponding speed of the electron in $3^{rd}$ orbit, in m/s is [2023]

Q 27 :

The radius of electron’s second stationary orbit in Bohr’s atom is R. The radius of 3rd orbit will be [2023]