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Question: If l<sub>1</sub> and l<sub>2</sub> denote the wavelengths of de-Broglie waves for electrons in the f...

If l1 and l2 denote the wavelengths of de-Broglie waves for electrons in the first and second Bohr orbits in hydrogen atom, then l1/l2 is equal to –

A

2/1

B

1/2

C

1/4

D

4/1

Answer

1/2

Explanation

Solution

λ1λ2\frac{\lambda_{1}}{\lambda_{2}}=hmv1hmv2\frac{\frac{h}{mv_{1}}}{\frac{h}{mv_{2}}}=v2v1\frac{v_{2}}{v_{1}}=Z/n2Z/n1\frac{Z/n_{2}}{Z/n_{1}}=n1n2\frac{n_{1}}{n_{2}}=12\frac{1}{2}