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Atoms

Question

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Wavelength of light emitted from second orbit to first orbit in a hydrogen atom is

6563 A^o

4102 A^o

4861 A^o

1215 A^o

Solution

D.

1215 A^o

The Rydberg formula is

$\frac{hc}{λ_{if}} = \frac{m e^{4}}{8 ε_{0}^{2} h^{2}} (\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}})$

where R = $\frac{{me}^{4}}{8 ε_{o}^{2} h^{3} c}$

Wavelength of light

$\frac{1}{λ} = R (\frac{1}{1^{2}} - \frac{1}{2^{2}})$

Where R is Rydberg constant

⇒ $\frac{1}{λ} = 1.097 \times 10^{7} \times \frac{3}{4}$

∴ λ = 1.215 × 10^-7 m

λ = 1215 A^o

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