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Question

Difference between nth and (n+2)th Bohr's radius of H atom is equal to its (n−2)th Bohr's radius. The value of n is:

A
4
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B
5
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C
6
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D
8
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Solution

The correct option is D 8
As per the question, for H atom
rn+2rn=rn2 ...(i)
where rn=Radius of Bohr's nth energy level
As per Bohr's theory, rn=0.529n2Z
For H atom, rn=0.529 n2
Similiarly, rn+2=0.529(n+2)2
rn2=0.529(n2)2
Putting these values in equation (i), we get
0.529(n+2)20.529 n2=0.529(n2)2
(n+2)2n2=(n2)2
n28n=0
n(n8)=0
n=0 or n=8
Since n=0 is not possible, the only possible value is n=8.

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