Atomic Structure | Physics JEE previous year questions with Solutions

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]

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

1

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 Bhor'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 Statemen I and Statement II are correct.
Statement I is incorrect but State II is correct.
Statement I is correct but State II is incorrect.
Both Statemen I and Statement II are incorrect.

1

2

3

4

(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]

0%

2

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

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

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

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

Topic Question Set

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]

0%

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Topic Question Set

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]

0%

Want Us to Email you About Special Offers & Updates?

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]