The first three spectral lines of H -atom in the Balmer series ar… - Vidyadip

MCQ

The first three spectral lines of $H$ -atom in the Balmer series are given $\lambda_{1}, \lambda_{2}, \lambda_{3}$ considering the Bohr atomic model, the wave lengths of first and third spectral lines $\left(\frac{\lambda_{1}}{\lambda_{3}}\right)$ are related by a factor of approximately 'x' $\times 10^{-1}$. The value of $x$, to the nearest integer, is

A
$20$
B
$22$
C
$25$
✓
$15$

✓

Answer

Correct option: D.

$15$

d
For 1 st line

$\frac{1}{\lambda_{1}}= R z^{2}\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)$

$\frac{1}{\lambda_{1}}= R z^{2} \frac{5}{36}$ ........$(i)$

For $3^{\text {rd }}$ line

$\frac{1}{\lambda_{3}}= Rz ^{2}\left(\frac{1}{2^{2}}-\frac{1}{5^{2}}\right)$

$\frac{1}{\lambda_{3}}= Rz ^{2} \frac{21}{100}$ $.........(ii)$

(ii) $+( i )$

$\frac{\lambda_{1}}{\lambda_{3}}=\frac{21}{100} \times \frac{36}{5}=1.512=15.12 \times 10^{-1}$

$x \approx 15$

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