Question

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

- 1
- 2
- 3
- 4

Solution

The correct option is **D** 4

As per the question, for H atom

rn+1−rn=rn−1 ...(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

rn−1=0.529(n−1)2

Putting these values in equation (i), we get

0.529(n+1)2−0.529 n2=0.529(n−1)2

⇒(n+1)2−n2=(n−1)2

⇒n2−4n=0

⇒n(n−4)=0

⇒n=0 or n=4

Since n=0 is not possible, the only possible value is n=4.

As per the question, for H atom

rn+1−rn=rn−1 ...(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

rn−1=0.529(n−1)2

Putting these values in equation (i), we get

0.529(n+1)2−0.529 n2=0.529(n−1)2

⇒(n+1)2−n2=(n−1)2

⇒n2−4n=0

⇒n(n−4)=0

⇒n=0 or n=4

Since n=0 is not possible, the only possible value is n=4.

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