JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Atomic Structure

According to Bohr's model of hydrogen atom, which of the following statement is incorrect?

(A)Radius of $3^{rd}$ orbit is nine times larger than that of $1^{st}$ orbit.
(B)Radius of $8^{th}$ orbit is four times larger than that of $4^{th}$ orbit.
(C)Radius of $6^{th}$ orbit is three time larger than that of $4^{th}$ orbit.✓ Correct
(D)Radius of $4^{th}$ orbit is four times larger than that of $2^{nd}$ orbit.

Answer: (C)

Solution

In Bohr's model the orbit radius grows as the square of the quantum number,

r_{n} \propto n^{2}

. The third orbit is

9

times the first, the eighth is

64/16 = 4

times the fourth, and the fourth is

16/4 = 4

times the second, each as stated. The sixth orbit, however, is

36/16 = 2.25

times the fourth, not three times, so the comparison of the sixth and fourth orbits is the incorrect statement.

JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Single correct option