Question

In Bohr's model of hydrogen atom, which of the following is an integral multiple of \(\dfrac{h}{2\pi}\) ?

• A. Kinetic energy of electron
• B. Radius of an atom
• C. Potential energy of electron
• D. Angular momentum of electron

Hint:

Bohr's quantisation rule: mvr = nh/2pi.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Bohr's model has one special rule that limits the electron to certain orbits. We must find which quantity is a whole-number multiple of \(h/2\pi\).

Step 2: Key Formula or Approach:
Bohr's quantisation condition says the angular momentum of the electron in an allowed orbit is \[ L = m v r = \frac{n h}{2\pi}, \quad n = 1, 2, 3, \ldots \]

Step 3: Apply the Condition:
The right side is n times \(h/2\pi\), with n a whole number. So the angular momentum is an integral multiple of \(h/2\pi\).

Step 4: Check Each Option:
Option 1: kinetic energy is \(13.6/n^2\) eV. It depends on \(1/n^2\), not on n times \(h/2\pi\). Wrong.
Option 2: the radius is \(r_n \propto n^2\). It is measured in metres, not in units of \(h/2\pi\). Wrong.
Option 3: potential energy is \(-27.2/n^2\) eV. Wrong.
Option 4: angular momentum is \(nh/2\pi\). Correct.

Final Answer:
Only the angular momentum of the electron is quantised as \(nh/2\pi\), so option 4 is correct. \[ \boxed{\text{Angular momentum of electron}} \]