Quantum Physics — practice questions

Light of frequency $6.00\times10^{14}$ Hz falls on a metal with work function $W_0 = 1.90$ eV.

Calculate the photon energy in eV, and state whether photoelectrons are emitted.

A metal's threshold frequency is $f_0 = 5.50\times10^{14}$ Hz. Light of frequency $7.20\times10^{14}$ Hz is incident on it.

Calculate the work function of the metal in eV, and the stopping voltage for the emitted electrons.

The intensity of light incident on a metal surface is doubled, while its frequency (above threshold) is kept constant. Explain, using the photon model, what happens to the photoelectric current and to the maximum kinetic energy of the emitted electrons — and explain why a wave model of light could not predict this result correctly.

An electron has momentum $p = 5.00\times10^{-24}$ kg m s⁻¹.

Calculate its de Broglie wavelength.

A proton ($m = 1.67\times10^{-27}$ kg) is accelerated from rest through a potential difference of $500$ V, gaining kinetic energy $E_k = eV = 500$ eV $= 8.01\times10^{-17}$ J.

Calculate the proton's speed and its de Broglie wavelength.

Explain how electron diffraction provides evidence for wave–particle duality, and explain why this effect is never observed for everyday macroscopic objects such as a thrown ball.

An electron drops from an energy level of $-1.5$ eV to $-3.4$ eV, emitting a photon.

Calculate the energy of the emitted photon in eV.

A hydrogen atom has energy levels including $E_2 = -3.40$ eV and $E_4 = -0.85$ eV. An electron absorbs a photon and moves from $E_2$ to $E_4$.

Calculate the frequency of the absorbed photon.

Explain why a hot gas produces bright emission lines at exactly the same frequencies as the dark absorption lines produced when the same (cooler) gas is placed in front of a continuous light source, and explain why only these specific frequencies appear rather than a continuous spectrum.