Given below are two statements: Statement I: The Balmer spectral line for H atom with lowest energy is located at ( = Rydberg constant). Statement II: When the temperature of black body increases, the maxima of the curve (intensity of wavelength) shift

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Solution

Q.
Given below are two statements:

Statement I: The Balmer spectral line for H atom with lowest energy is located at $\frac{5}{36} R_{H} {cm}^{- 1}$
( $R_{H}$ = Rydberg constant).

Statement II: When the temperature of black body increases, the maxima of the curve (intensity of wavelength) shifts to shorter wavelength.

In the light of the above statements choose the correct answer from the options given below. [2024]

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 true.

4 Both Statement I and Statement II are false.

Ans.
(3)

At a given temperature, intensity of radiation emitted increases with the increase of wavelength, reaches a maximum value at a given wavelength and then starts decreasing with further increase of wavelength. Also, as the temperature increases, maxima of the curve shifts to short wavelength.

For Balmer spectral line of H-atom with lowest energy, $n_{1} = 2$ and $n_{2} = 3$

$\bar{ν} = 109, 677 (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) {cm}^{- 1}$

$\bar{ν} = R_{H} (\frac{1}{4} - \frac{1}{9}) = R_{H} (\frac{9 - 4}{36}) = R_{H} (\frac{5}{36}) c m^{- 1}$

Where 109,677 = $R_{H}$ (Rydberg constant)

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