The angular momentum of an electron in a hydrogen atom is proportional to : (Where r is the radius of orbit of electron)

Solution

Physics sir · 4 steps

Link both L and r to the same n, then eliminate n to see how L grows with r.

1. Two Bohr results. Bohr's quantisation rule gives L = nh/2π, so L ∝ n. The orbit radius is r = 0.529 n² Å for hydrogen, so r ∝ n².
2. Eliminate n. From r ∝ n² you get n ∝ √r. Put this into L ∝ n.

   L ∝ n ∝ √r

3. Check with forces. The Coulomb force supplies the centripetal force: mv²/r = ke²/r², so v ∝ 1/√r. Then L = mvr ∝ 1/√r × r = √r, the same result.
4. So. The angular momentum is proportional to √r, which is option (c).

The idea to keep. In Bohr questions, write every quantity as a power of n first (L ∝ n, r ∝ n², v ∝ 1/n). Then any one can be expressed in terms of another in one line.

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