Difference between nth and (n + 1)th Bohr’s radius of hydrogen atom is equal to (n – 1)th Bohr’s radius. The value of n is

Q. Difference between nth and (n + 1)th Bohr’s radius of hydrogen atom is equal to (n – 1)th Bohr’s radius. The value of n is

(a) 1

(b) 2

(c) 3

(d) 4

Ans: (d)

Sol: r_n ∝  n²

r_n+1 ∝ (n+1)²

r_n-1 ∝ (n-1)²

A/c to question ,

(n+1)² – n² = (n-1)²

2n + 1 = n² – 2n +1

n² – 4n = 0

n(n-4) = 0
n = 4