Statement I : When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules dissociate and the energetically excited hydrogen a

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Solution

Q.
Given below are two statements:

Statement I : When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules dissociate and the energetically excited hydrogen atoms produce electromagnetic radiation of discrete frequencies.

Statement II : The frequency of second line of Balmer series obtained from ${He}^{+}$ is equal to that of first line of Lyman series obtained from hydrogen atom.

In the light of the above statements, choose the correct answer from the options given below : [2026]

1 Statement I is true but Statement II is false

2 Statement I is false but Statement II is true

3 Both Statement I and Statement II are false

4 Both Statement I and Statement II are true

Ans.
(4)

$\frac{1}{λ} = R Z^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$

For 1st line of Lyman series in H-atom

$\frac{1}{λ} = R {(1)}^{2} (\frac{1}{1^{2}} - \frac{1}{2^{2}})$

$\frac{1}{λ} = \frac{3 R}{4}$

For 2nd line of Balmer series of ${He}^{+}$

$\frac{1}{λ'} = R {(2)}^{2} (\frac{1}{2^{2}} - \frac{1}{4^{2}})$

$\frac{1}{λ'} = \frac{3 R}{4}$

As $λ$ and $λ'$ are equal, so frequency of these lines will also be equal.

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