QJEEM21Ph5613: JEE Main 2021 Physics - Class 12 JEEM21Ph5613 Solution: The first three spectral lines of H-atom in the Balmer series…

Question

Verified Solution • 2025–26 Session moderate

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

λ

₁,

λ

₂,

λ

₃ considering the Bohr atomic model, the wave lengths of first and third spectral lines

(\frac{λ_{1}}{λ_{3}})

are related by a factor of approximately 'x'

\times

10^{$-$ 1}.

The value of x, to the nearest integer, is _________.

Accepted Answer

For 1^st line

\frac{1}{λ_{1}} = R z^{2} (\frac{1}{2^{2}} - \frac{1}{3^{2}})

\frac{1}{λ_{1}} = R z^{2} \frac{5}{36}

..... (i)

For 3^rd line

\frac{1}{λ_{3}} = R z^{2} (\frac{1}{2^{2}} - \frac{1}{5^{2}})

\frac{1}{λ_{3}} = R z^{2} \frac{21}{100}

...... (ii)

Dividing (ii) by (i),

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

x \approx 15

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