Quantum Mechanics Questions and Answers

Answer: C

The correct matching is P-3, Q-4, R-2, S-1.

• The Stern-Gerlach experiment split a beam of silver atoms, which have no orbital angular momentum in their ground state, into two: evidence for electron spin (P-3).
• The Zeeman effect, the splitting of spectral lines in a magnetic field into discrete components, shows that the orientation of angular momentum is quantized, that is, space quantization (Q-4).
• The Franck-Hertz experiment found electrons losing energy to mercury atoms only in fixed amounts, showing quantized atomic energy levels (R-2).
• The Davisson-Germer experiment diffracted electrons from a nickel crystal, demonstrating the wave nature of particles (S-1).

Stern-Gerlach is sometimes also cited for space quantization, but in this set the only match leaving every inference used once pairs it with spin. The other options misassign Davisson-Germer or Franck-Hertz, whose inferences are unambiguous.

Answer: D

The ratio is 16.

In the Bohr model the kinetic energy of the electron in the nth orbit is \(T_{n} = \frac{13.6}{n^{2}}\) eV, so it falls as \(1/n^{2}\). The ground state is \(n = 1\); the first, second and third excited states are \(n = 2, 3, 4\).

\[ \frac{T_{g}}{T_{e}} = \frac{1/1^{2}}{1/4^{2}} = 16 \]

Taking the third excited state as \(n = 3\) gives 9, the commonest slip. 4 and 3 come from using \(n\) instead of \(n^{2}\).