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

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Q.
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]

1 Both Statement I and Statement II are correct.

2 Statement I is incorrect but Statement II is correct.

3 Statement I is correct but Statement II is incorrect.

4 Both Statement I and Statement II are incorrect.

Ans.
(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 $\frac{h}{2 π}$

Solution

1 Both Statement I and Statement II are correct.

2 Statement I is incorrect but Statement II is correct.

3 Statement I is correct but Statement II is incorrect.

4 Both Statement I and Statement II are incorrect.

Ans.
(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 $\frac{h}{2 π}$

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Solution

1 Both Statement I and Statement II are correct.

2 Statement I is incorrect but Statement II is correct.

3 Statement I is correct but Statement II is incorrect.

4 Both Statement I and Statement II are incorrect.

Ans. (3) E = hf ML2T–2=[h]×[T–1] [h]=[ML2T–1] L=[MVR]=[ML2T–1] L=nh2π L is integral multiple of h2π

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Ans.
(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 $\frac{h}{2 π}$