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MODEL PAPER 5 — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMODEL PAPER 53 Marks
Question
An electron in a hydrogen atom makes transitions from orbits of higher energies to orbits of lower energies.
a. When will such transitions result in (a) Lyman (b) Balmer series?
b. Find the ratio of the longest wavelength in Lyman series to the shortest wavelength in Balmer series.
✓

Answer

a. Transition result in Lyman series if electron will jump from a higher energy orbit to n = 1 orbit
Transition result in Balmer series if electron will jump from a higher energy orbit to n = 2 orbit Image
b. Longest wavelength in Lyman Series
$\frac{1}{\lambda_L}=R \cdot\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]=R\left[\frac{1}{1^2}-\frac{1}{2^2}\right]=\frac{3 R}{4}$
Shorted wavelength in Balmer Series
$\frac{1}{\lambda_S}=R\left[\frac{1}{n_1{ }^2}-\frac{1}{n_2^2}\right]=R\left[\frac{1}{2^2}-\frac{1}{\infty}\right]=\frac{R}{4}$
Ratio $\frac{\lambda_2}{\lambda_S}=\frac{4}{3 R} \times \frac{R}{4}=\frac{1}{3}$

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