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Question

If $$\lambda_1$$ and $$\lambda_2$$ denote the wavelengths of de Broglie waves for electrons in the first and second Bohr orbits in a hydrogen atom, then $$\lambda_1/\lambda_2$$ is equal to :


A
2
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B
12
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C
14
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D
4
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Solution

The correct option is B $$\dfrac{1}{2}$$
The De-Broglie wavelengths can be given by:

$$\lambda =\dfrac{h}{mv}..(1)$$

Since mass of electron remains same, we get

$$\dfrac{\lambda _{1}}{\lambda _{2}}=\dfrac{v_{2}}{v_{1}}..(2)$$

Now, by Bohr's postulates, we know that velocity of electron in $$n^{th}$$ orbit in inversely proportional to $$n$$.

 Hence, Answer= $$1/2$$.

Physics

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