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Difference between nth and (n+1)th Bohr's radius of H atom is equal to its (n1)th Bohr's radius. The value of n is:
  1. 1
  2. 2
  3. 3
  4. 4


Solution

The correct option is D 4
As per the question, for H atom
rn+1rn=rn1   ...(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+1=0.529(n+1)2
                 rn1=0.529(n1)2
Putting these values in equation (i), we get
0.529(n+1)20.529 n2=0.529(n1)2
(n+1)2n2=(n1)2
n24n=0
n(n4)=0
n=0 or n=4
Since n=0 is not possible, the only possible value is n=4.

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