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Question

The de-broglie wavelength of an electron in the 3rd orbit of hydrogen atom is

A
9.97A0
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B
8.0A0
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C
10.20A0
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D
12.80A0
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Solution

The correct option is A 9.97A0
Radius of 3rd orbit =r=R(3)2
=9R
[Here R= Radius of first orbit of hydrogen atom]
mvr=nh/(2π)
h/(mv)=2πr/n
λ=h/(mv)=2π×9R/3
λ=6πR
λ=6π×(0.529Å)
λ=9.97Å
De-Broglie wavelength is 9.97Å
Hence,
option (A) is correct answer.

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