Question

The difference in angular momentum of electron between two successive orbits of hydrogen atom is

• A. \(\frac{h}{2\pi}\)
• B. \(\frac{h}{\pi}\)
• C. \(\frac{h}{2}\)
• D. 2h

Hint:

Remember Bohr's three postulates:
(1) Electrons revolve in stable circular orbits without radiating energy.
(2) Angular momentum is quantized: \(L = n\hbar\).
(3) Energy is radiated/absorbed when an electron jumps between orbits, with frequency \(f = \frac{\Delta E}{h}\).
The difference in angular momentum between any two consecutive orbits is always \(\hbar\) or \(\frac{h}{2\pi}\).

Answer 1

The Correct Option is A

Step 1: Recall the reduced Planck constant.
Bohr's model says the allowed angular momenta are integer multiples of \(\hbar = h/2\pi\). That is, \(L = n\hbar\) with \(n\) a whole number.

Step 2: Picture the ladder of values.
The permitted angular momenta form a ladder: \(\hbar, 2\hbar, 3\hbar, \dots\) The rung spacing is constant.

Step 3: Read off the spacing.
Going from one orbit to the very next always adds exactly one \(\hbar\), so the gap between successive orbits is \(\hbar = h/2\pi\), no matter which pair of neighbouring orbits you choose.

Step 4: Conclude.
Hence the difference in angular momentum between two consecutive Bohr orbits is \(h/2\pi\).
\[\boxed{\Delta L = h/2\pi}\]