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Particle-Wave Duality Physics

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Particle-Wave Duality Physics

Investigate how light and matter reveal both wave-like and particle-like behaviour. Show working for calculations, use SI units, and give answers to an appropriate number of significant figures.

Light behaving as particles

A materials lab tests a metal photocathode using different light frequencies.

1.The metal has a work function of 2.30 eV. Which statement best defines its threshold frequency?

The greatest frequency that can produce photoelectrons
The smallest frequency that can produce photoelectrons
The frequency at which emitted electrons have maximum kinetic energy
The frequency of the electrons after emission

2.Light of frequency 8.0 × 10¹⁴ Hz shines on the photocathode. Calculate the maximum kinetic energy of the emitted electrons in eV. Use h = 6.63 × 10⁻³⁴ J s and 1 eV = 1.60 × 10⁻¹⁹ J. Show your working.

3.For the photocathode in Question 1, calculate the threshold frequency. Give your answer to 3 significant figures. Use h = 6.63 × 10⁻³⁴ J s and 1 eV = 1.60 × 10⁻¹⁹ J.

4.A student increases the intensity of light but keeps its frequency below the threshold frequency. What happens to photoelectron emission? Explain briefly.

5.A stopping potential of 1.25 V is measured in a photoelectric experiment. Find the maximum kinetic energy of the photoelectrons in joules and in eV.

Discrete energy and matter waves

Use energy changes and de Broglie wavelength to interpret evidence from atoms and electrons.

6.In a hydrogen atom, an electron falls from −1.51 eV to −3.40 eV. Calculate the frequency of the emitted photon. Use h = 6.63 × 10⁻³⁴ J s and 1 eV = 1.60 × 10⁻¹⁹ J.

7.Choose the correct explanation of the line spectrum produced by excited hydrogen atoms.

The electron can lose any amount of energy, so the spectrum is continuous
Only particular energy changes are possible, so photons have particular energies
Every hydrogen atom emits photons of the same energy regardless of the transition
The lines are caused by electrons behaving as sound waves

8.An electron travels at 2.0 × 10⁶ m s⁻¹. Calculate its de Broglie wavelength. Use h = 6.63 × 10⁻³⁴ J s and electron mass mₑ = 9.11 × 10⁻³¹ kg.

9.In an electron diffraction experiment, electrons strike a screen and form a pattern of rings. The spacing of the rings depends on the diffraction angle. If the electron momentum is increased, what happens to the de Broglie wavelength, and how does this affect the scale of the diffraction pattern?

10.A colleague claims: “The photoelectric effect proves light is only a particle, and electron diffraction proves electrons are only waves.” Explain why this conclusion is not justified. Include what each experiment demonstrates.