Atomic Structure | Physics JEE previous year questions with Solutions

Q 11 :

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 ( $h = 6.62 \times 10^{- 34} Js$ ) [2023]

D
B
A
C

1

2

3

4

(1)

$λ = \frac{h c}{Δ E}$

$Δ E_{A} = 2.2 eV$

$Δ E_{B} = 5.2 eV$

$Δ E_{C} = 3 eV$

$Δ E_{D} = 10 eV$

$λ_{A} = \frac{6.62 \times 10^{- 34} \times 3 \times 10^{8}}{2.2 \times 1.6 \times 10^{- 19}} = \frac{12.41 \times 10^{- 7}}{2.2} m = 564 nm$

$λ_{B} = \frac{1241}{5.2} nm = 238.65 nm$

$λ_{C} = \frac{1241}{3} nm = 413.66 nm$

$λ_{D} = \frac{1241}{10} nm = 124.1 nm$

Q 12 :

An electron of a hydrogen like atom, having Z = 4, jumps in from $4^{th}$ energy state to $2^{nd}$ energy state. The energy released in this process, will be: (Given $R_{c h} = 13.6 eV$ ) Where R = Rydberg constant c = Speed of light in vacuum h = Planck's constant [2023]

13.6 eV
10.5 eV
3.4 eV
40.8 eV

1

2

3

4

(4)

$Δ E = 13.6 Z^{2} [\frac{1}{2^{2}} - \frac{1}{4^{2}}] eV$

$= 13.6 \times {(4)}^{2} (\frac{1}{4} - \frac{1}{16}) eV$

$= 13.6 [4 - 1] eV = 13.6 \times 3 = 40.8 eV$

Q 13 :

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is [2023]

C
A
D
B

1

2

3

4

(3)

$Δ E = \frac{h c}{λ} \Rightarrow λ \propto \frac{1}{Δ E}$

For shortest wavelength, energy gap should be maximum.

So, correct choice is transition from $n = 3$ to $n = 1$ .

Q 14 :

The angular momentum for the electron in Bohr’s orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be [2023]

$\frac{L}{2}$
$zero$
$L$
$2 L$

1

2

3

4

(3)

$L = m v r, r \propto n^{2}, v \propto \frac{1}{n}$
$∴$ $L \propto n$

Also, $L = \frac{n h}{2 π}$ ,

Bohr orbit is, $L_{1} = L = \frac{1 h}{2 π}$

$L_{2} = 2 [L] = 2 L$

$L_{2} = \frac{2 h}{2 π}$

So change = $L_{2} - L_{1} = 2 L - L = L$

Q 15 :

The energy of ${He}^{+}$ ion in its first excited state is. [2023]

(The ground state energy for the Hydrogen atom is −13.6 eV)

−3.4 eV
−54.4 eV
−13.6 eV
−27.2 eV

1

2

3

4

(3)

$E_{a} = \frac{- 13.6 Z^{2}}{n^{2}} = \frac{- 13.6 \times 4}{4} = - 13.6 eV$

Q 16 :

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be [2023]

2
1
3
4

1

2

3

4

(3)

According to Bohr's postulates, an electron makes jump to higher energy orbital if it absorbs a photon of energy equal to difference between the energies of an excited state and the ground state. Assuming that collided electron takes energy equal to 10.2 eV or 12.09 eV from the incoming electron beam (some part lost due to collision). The maximum excited state is $n = 3$ . So, number of spectral lines $= \frac{3 (3 - 1)}{2} = 3$

Q 17 :

For hydrogen atom, $λ_{1}$ and $λ_{2}$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of $λ_{1}$ and $λ_{2}$ is $\frac{x}{32}$ . The value of $x$ is _________. [2023]

0%

(27)

$\frac{1}{λ} = R z^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$

$\frac{1}{λ_{1}} = R z^{2} [\frac{1}{1^{2}} - \frac{1}{3^{2}}] = \frac{8}{9} R z^{2} \dots (1)$

$\frac{1}{λ_{2}} = R z^{2} [\frac{1}{1^{2}} - \frac{1}{2^{2}}] = \frac{3}{4} R z^{2} \dots (2)$

$\frac{1}{2} \Rightarrow \frac{λ_{2}}{λ_{1}} = \frac{8}{9} \times \frac{4}{3} = \frac{32}{27} \Rightarrow \frac{λ_{1}}{λ_{2}} = \frac{27}{32}$

Q 18 :

The wavelength of the radiation emitted is $λ_{0}$ 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 $\frac{20}{x} λ_{0}$ . The value of $' x'$ is ________. [2023]

0%

(27)

$\frac{1}{λ_{0}} = R [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$

$\frac{1}{λ_{0}} = R [\frac{1}{4} - \frac{1}{9}] = \frac{5 R}{36} \dots (i)$

$\frac{1}{λ} = R [\frac{1}{4} - \frac{1}{16}] = \frac{3 R}{16} \dots (i i)$

$\frac{1}{2} \Rightarrow \frac{λ}{λ_{0}} = \frac{5}{36} \times \frac{16}{3} = \frac{20}{27}$

Q 19 :

The radius of fifth orbit of the ${Li}^{+ +}$ is _______ $\times 10^{- 12} m$ .

Take: radius of hydrogen atom $= 0.51 Å$ . [2023]

0%

(425)

$r_{n} = r_{0} \frac{n^{2}}{Z} \Rightarrow r_{n} = 0.51 \times \frac{25}{3} Å = 4.25 \times 10^{- 10} m$

Q 20 :

The ratio of wavelength of spectral lines $H_{α}$ and $H_{β}$ in the Balmer series is $\frac{x}{20}$ . The value of $x$ is ________. [2023]

0%

(27)

$\frac{1}{λ} = R [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] for H-atom$

$For Balmer series, n_{1} = 2$

$\frac{1}{λ} = R [\frac{1}{4} - \frac{1}{n_{2}^{2}}]$

$For H_{α}, n_{2} = 3 and H_{β}, n_{2} = 4$

$\frac{1}{λ_{H_{α}}} = R [\frac{1}{4} - \frac{1}{9}] = \frac{5 R}{36}$

$\frac{1}{λ_{H_{β}}} = R [\frac{1}{4} - \frac{1}{16}] = \frac{3 R}{16}$

$\frac{\frac{1}{λ_{H_{α}}}}{\frac{1}{λ_{H_{β}}}} = \frac{\frac{5 R}{36}}{\frac{3 R}{16}}$

$\Rightarrow \frac{λ_{H_{α}}}{λ_{H_{β}}} = \frac{27}{20} = \frac{x}{20} \Rightarrow x = 27$

Topic Question Set

Q 11 :

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 ( $h = 6.62 \times 10^{- 34} Js$ ) [2023]

Q 12 :

An electron of a hydrogen like atom, having Z = 4, jumps in from $4^{th}$ energy state to $2^{nd}$ energy state. The energy released in this process, will be: (Given $R_{c h} = 13.6 eV$ ) Where R = Rydberg constant c = Speed of light in vacuum h = Planck's constant [2023]

Q 13 :

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is [2023]

Q 14 :

The angular momentum for the electron in Bohr’s orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be [2023]

Q 15 :

The energy of ${He}^{+}$ ion in its first excited state is. [2023]

(The ground state energy for the Hydrogen atom is −13.6 eV)

Q 16 :

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be [2023]

Q 17 :

For hydrogen atom, $λ_{1}$ and $λ_{2}$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of $λ_{1}$ and $λ_{2}$ is $\frac{x}{32}$ . The value of $x$ is _________. [2023]

0%

0%

Q 19 :

The radius of fifth orbit of the ${Li}^{+ +}$ is _______ $\times 10^{- 12} m$ .

Take: radius of hydrogen atom $= 0.51 Å$ . [2023]

0%

Q 20 :

The ratio of wavelength of spectral lines $H_{α}$ and $H_{β}$ in the Balmer series is $\frac{x}{20}$ . The value of $x$ is ________. [2023]

0%

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