The first three spectral lines of H-atom in the Balmer series are given

Question:

The first three spectral lines of $\mathrm{H}$-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 afactor of approximately ' $x^{\prime} \times 10^{-1}$

.The value of $\mathrm{x}$, to the nearest integer, is

Solution:

$(15)$

For 1 st line

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

$\frac{1}{\lambda_{1}}=\mathrm{Rz}^{2} \frac{5}{36}$

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

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

$\frac{1}{\lambda_{3}}=\mathrm{R} z^{2} \frac{21}{100}$

(ii) $+(\mathrm{i})$

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

$\mathrm{x} \approx 15$

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