According to Bohr's atomic theory :
(A) Kinetic energy of electron is ∝ Z²/n².
(B) The product of velocity (v) of electron and principal quantum number (n), 'vn' ∝ Z².
(C) Frequency of revolution of electron in an orbit is ∝ Z³/n³.
(D) Coulombic force of attraction on the electron is ∝ Z³/n⁴.
Choose the most appropriate answer from the options given below :

Solution

Chemistry ma’am · 3 steps

Write down how r and v depend on Z and n, and every other Bohr quantity follows from those two.

1. The two basics. In Bohr's model the orbit radius is r ∝ n²/Z and the electron's speed is v ∝ Z/n. Build each statement from these.

   Statement	Build it from r and v	Result	Verdict
   (A) Kinetic energy	1/2mv² ∝ (Z/n)²	∝ Z²/n²	correct
   (B) vn	Z/n × n	∝ Z, not Z²	wrong
   (C) Frequency	v/(2π r) ∝ (Z/n)/(n²/Z)	∝ Z²/n³, not Z³/n³	wrong
   (D) Coulombic force	kZe²/r² ∝ Z × Z²/n⁴	∝ Z³/n⁴	correct

2. Watch the extra Z. In the force, one Z comes from the nuclear charge Ze and two more come from 1/r². That is why the force has Z³.
3. So. Only (A) and (D) are correct, which is option (d).

The idea to keep. Learn just two results by heart: r ∝ n²/Z and v ∝ Z/n. Energy, frequency, force and time period can all be built from these two in one line.

Answer from the NTA final answer key. Solution by PrepWiser.