Free Dawn of Modern Physics MCQs with Answers

1. Planck's quantum theory proposed that energy is emitted or absorbed

• A. continuously in any amount
• B. in discrete packets called quanta, each of energy hf
• C. only as heat
• D. only by solids

Explanation: Planck found that black body radiation could only be explained if the energy came in multiples of hf, where h is Planck's constant and f the frequency. Classical physics assumed a continuous exchange and predicted infinite energy at short wavelengths, the so called ultraviolet catastrophe. Quantisation resolved that failure and began quantum physics.

2. The energy of a photon is given by

• A. hf
• B. h divided by f
• C. hc
• D. mc squared only

Explanation: Energy is Planck's constant multiplied by frequency, equivalently hc divided by wavelength, so shorter wavelength means more energetic photons. This is why ultraviolet light damages skin while visible light of the same intensity does not. Planck's constant is 6.63 times 10 to the minus 34 joule seconds.

3. In the photoelectric effect, electrons are emitted from a metal surface only if the incident light has

• A. sufficient intensity, whatever its frequency
• B. a frequency above a threshold value characteristic of the metal
• C. been shone for long enough
• D. a long wavelength

Explanation: Below the threshold frequency no electrons are emitted however bright the light or however long it shines, which the wave theory could not explain and which the photon picture explains at once: one photon must carry enough energy on its own to free one electron. Raising the intensity above threshold increases the number of electrons but not their maximum energy. Emission is also immediate, with no time lag.

4. In the photoelectric effect, increasing the intensity of the incident light while keeping the frequency fixed increases

• A. the maximum kinetic energy of the emitted electrons
• B. the number of electrons emitted per second
• C. the threshold frequency
• D. the work function of the metal

Explanation: More intense light means more photons per second, so more electrons are ejected, but each photon still carries the same energy hf and so gives each electron the same maximum kinetic energy. Only raising the frequency raises that energy. The failure of the wave theory to predict this is the strongest evidence for the particle nature of light.

5. Einstein's photoelectric equation states that the maximum kinetic energy of an emitted electron is

• A. hf plus the work function
• B. hf minus the work function
• C. the work function minus hf
• D. hf multiplied by the work function

Explanation: The photon energy hf is spent first on freeing the electron from the metal, which costs the work function, and whatever remains appears as kinetic energy. If hf is less than the work function nothing is emitted at all, which defines the threshold frequency. A graph of maximum kinetic energy against frequency is a straight line of gradient h.

6. The work function of a metal is

• A. the minimum energy needed to remove an electron from its surface
• B. the energy of the incident photon
• C. the kinetic energy of the fastest emitted electron
• D. the total energy of all the electrons

Explanation: Work function is a property of the metal, usually quoted in electron volts, and metals such as caesium with low values emit electrons even in visible light while most need ultraviolet. Dividing the work function by Planck's constant gives the threshold frequency. It corresponds to electrons at the surface, which is why the equation gives the maximum rather than the typical kinetic energy.

7. The Compton effect, in which X rays scattered by electrons emerge with a longer wavelength, demonstrates that photons

• A. have no momentum
• B. carry momentum and collide like particles
• C. travel slower than light
• D. have mass at rest

Explanation: The scattered photon gives up part of its energy and momentum to the recoiling electron, so its frequency falls and its wavelength rises, exactly as a particle collision would predict. A wave would have been scattered without any change of wavelength. Photon momentum is h divided by wavelength, even though the photon has zero rest mass.

8. According to de Broglie, the wavelength associated with a moving particle is

• A. h divided by its momentum
• B. h multiplied by its momentum
• C. hf
• D. c divided by its speed

Explanation: Wavelength is Planck's constant divided by mv, so heavy everyday objects have wavelengths far too small to detect while an electron's is comparable to atomic spacings. This is why electrons can be diffracted by a crystal, which was the experimental confirmation of the idea. The result gives every particle a wave aspect, completing the wave particle duality.

9. An electron microscope achieves much higher resolution than a light microscope because

• A. electrons travel faster than light
• B. the de Broglie wavelength of a fast electron is far shorter than the wavelength of visible light
• C. electrons are smaller than photons
• D. it uses a stronger lens

Explanation: Resolution is limited by wavelength, and accelerating electrons to high speed gives them a wavelength of the order of a picometre, thousands of times shorter than visible light. Magnetic lenses then focus them in place of glass. Electrons certainly do not travel faster than light, which rules out the first option immediately.

10. Wave particle duality means that

• A. light is a wave and matter is a particle, always
• B. light and matter each show wave behaviour in some experiments and particle behaviour in others
• C. waves and particles are the same thing in every respect
• D. particles travel in waves through a medium

Explanation: Interference and diffraction reveal the wave nature of light, while the photoelectric and Compton effects reveal its particle nature, and electron diffraction shows that matter behaves the same way. Which aspect appears depends on the experiment performed, and no single experiment shows both at once. This complementarity is a foundation of quantum mechanics.