### H2 Physics Quantum Physics Common Questions and Answers

Definitions

1. Photoelectric effect – The emission of electrons from a cold metal surface when electromagnetic radiation of a sufficiently high frequency falls on it
2. Stopping potential (Vs) – Minimum potential difference between the cathode and the anode that will prevent the most energetic photoelectron emitted from the cathode from reaching the anode
3. Photon – A discrete packet/quantum of energy of electromagnetic radiation
4. Work function – Minimum amount of energy required to remove the least tightly bound electron from the surface of a metal
5. Threshold frequency – Minimum frequency an EM radiation must possess to remove an electron from the surface of a metal to cause photoelectric emission
6. Wave-Particle duality – Matter behave like waves in some situations and like particles in others (Photoelectric effect provides the particulate nature; interference patterns produced in double-slit experiment explains wave nature)
7. de Broglie wavelength – Wavelength associated with a particle that is moving
8. Energy level – The energy of an electron in an isolated atom is quantised. The electron is allowed to exist in specific energy states known as energy levels.
9. Emission spectral lines – Bright coloured lines against a dark background. The spectra are line spectra as a result of the precise energy levels in the atom.
10. Absorption spectral lines – Dark lines against bright coloured background
11. Ground state – Electrons in the most stable lowest energy state/level (in an atomic orbit, according to Bohr’s atom model)
12. Heisenberg Uncertainty Principle – If a measurement of the position of a particle is made with uncertainty ∆x and a simultaneous measurement of its linear momentum is made with precision ∆p, then the product of the 2 uncertainties can never be smaller than h/4π (or ℏ/2π) ∆x∆p ≥ h/4π
13. Potential barrier – A region where there is a sudden increase in potential due to a field of force (usually electric) that exists and opposes the motion of a particle through the region.
14. Quantum tunnelling – (Based on classical mechanics, an electron with energy E should be unable to overcome a potential barrier if it does not have sufficient energy); Experimentally, some electrons can tunnel through the barrier at a probability given by its transmission coefficient T (represents the probability of the particle being transmitted through a rectangular barrier of height U and length U)

What are the 4 results of the photoelectric effect experiments?

1. Current is proportional to intensity. This result can be explained using wave nature and particulate nature of light.
2. For every material of cathode irradiated, there is a threshold frequency below which no electrons would be emitted from the cathode regardless of light intensity. This result can be explained using the particulate nature of light only.
3. The maximum kinetic energy of emitted photoelectrons depends only on the frequency of the incident radiation, and not its intensity. This result can be explained using the particulate nature of light only.
4. The emission of photoelectrons starts with no observable time lag, even for very low intensity of incident radiation. This result can be explained using the particular nature of light only.

Explain how spectral lines show discrete energy levels in an atom.

An emission spectrum consists of a set of discrete wavelengths. A photon is emitted from an isolated atom when one of its electrons transits from a higher to a lower energy level. Energy of the photon is equal to the energy difference between the two levels involved in the transition.

Distinguish between emission and absorption line spectra.

An emission line spectrum of an element consists of coloured lines on a dark background while an absorption spectrum consists of dark lines on a coloured background at the same discrete wavelength positions for the same element. For emission spectra, electrons transit from a higher energy level to a lower energy level. For absorption spectra, electrons transit from a lower energy level to a higher energy level.

Describe and interpret qualitatively the evidence provided by electron diffraction for the wave nature of particles.

When a beam of electrons passed through a thin film of crystal, the dispersion pattern of the emergent electrons produced on a screen is observed to be similar to the diffraction pattern produced by a beam of X-ray. This phenomenon provides evidence for the wave nature of particles like electrons.

Explain the different parts of the X-ray radiation intensity graph

• Formation: Electrons emitted by the heated filament are made to accelerate through a high PD before they collide with the metal target with very high speeds à interactions with the nuclei of the target atoms, thus electrons lose KE à KE lost converted to energy of x-ray photos radiated from the target; different electrons slowed to different extent à energies of x-ray photons produced take a continuous of values à continuous spectrum formed

The sharp characteristic peak (unique for each element)

• Occurs when bombarding electron colliding with a target atom has enough energy to remove an inner-shell electron from the atom
• Existence of Ka and Kb values: Incoming electron knocked off an electron in the n = 1 level (K-shell), in which the vacancy in this shell is then filled by an electron from the n = 2 L-shell, an x-ray photon of the Ka characteristic x-ray is emitted; For Kb, when the vacancy in the K-shell is filled by an electron dropping from the n = 3 M-shell, x-ray photon of the Kb characteristic x-ray is emitted
• Why is the intensity of the Ka characteristic x-ray > Kb characteristic x-ray: Electrons in the n = 2 L-shell are nearer to the n = 1 K-shell, thus there is a greater probability that the vacancy in the K-shell is filled by an electron from the L-shell than the n =3 M-shell.

Other points to note for X-rays:

• Same target material –> characteristic x-rays produced have same wavelengths –> energy levels of target atoms are the same
• Higher voltage applied in x-ray tube –> minimum wavelength of x-rays produced is lower –> bombarding electrons produced by tube have higher initial KE (ß with higher voltage applied)

Explain qualitatively the phenomenon of quantum tunneling of an electron across a potential barrier.

An electron is considered as a wave function. The probability of finding an electron is directly proportional to the square of the amplitude of the wave function. When the wave function of an electron encounters a potential barrier, its amplitude decreases exponentially. For a narrow barrier, the wave amplitude may not become zero after the electron passes through the barrier. Hence, there is a non-zero probability that the electron will be found beyond the barrier. This process is called quantum tunneling.

Why is it that sound waves are not normally considered as having particle-like properties, nor raindrops as having wave-like properties?

The wavelength of a wave is related to its momentum and the Planck constant by the equation l=h/mv. For sound waves, their wavelength is too long hence the sound particles have too little momentum to exhibit particulate properties. For raindrops, due to their large mass and hence momentum, their wavelength is too short for them to undergo significant diffraction. Diffraction can only be observable if the dimension of the aperture is comparable to the wavelength of the wave.