True or false on quantum physics

Problem

True or false?

• (a) The photoelectric effect shows the corpuscular character of light.
• (b) The stable orbits of the Bohr atom correspond to integer multiples of $h/(2\pi)$ of angular momentum.
• (c) The Davisson–Germer experiment reveals the corpuscular character of electrons.
• (d) The uncertainty principle is a fundamental limitation, not an instrumental one.
• (e) A blue-light photon has less energy than a red-light photon.

Solution

(a) TRUE. The photoelectric effect can only be explained with light quanta (photons) of energy $hf$ absorbed one at a time: it is proof of the corpuscular character of light.

(b) TRUE. Bohr’s condition is $L = m v r = n\hbar = n\,h/(2\pi)$: angular momentum is quantised in integer multiples of $\hbar = h/(2\pi)$.

(c) FALSE. Davisson–Germer observes the diffraction of electrons off crystals: it reveals the wave-like (not corpuscular) character of electrons, confirming de Broglie.

(d) TRUE. The uncertainty $\Delta x\,\Delta p \geq \hbar/2$ is a fundamental property of quantum nature, not an equipment flaw: it cannot be eliminated by improving the apparatus.

(e) FALSE. $E = hc/\lambda$: blue light has a smaller $\lambda$ than red, and hence greater energy. The statement is reversed.

$\ev{\text{(a) T,\quad (b) T,\quad (c) F,\quad (d) T,\quad (e) F}}$

Links

Topics: Quantum physics Concepts: Photoelectric effect · Bohr model · de Broglie wavelength · Uncertainty principle · Photon