Subject: Physics | Level: A-Level | Exam Board: AQA
This guide explores the pivotal experiments and theories that revolutionised physics, from the null result of the Michelson-Morley experiment to Einstein's theories of special relativity and the quantum nature of light. It's a crucial A-Level topic that bridges classical and modern physics, and mastering it is key to top marks.
Revision Notes & Key Concepts
Key Terms & Definitions
- Work Function (φ)
- The minimum energy required to remove a single electron from the surface of a particular metal.
- Threshold Frequency (f₀)
- The minimum frequency of incident electromagnetic radiation required to cause photoelectric emission from the surface of a particular metal.
- Proper Time (t₀)
- The time interval between two events measured by an observer for whom the events occur at the same position in space.
- Proper Length (L₀)
- The length of an object measured in the same rest frame as the object.
- Inertial Frame of Reference
- A frame of reference that is not accelerating (i.e., it is moving at a constant velocity).
- Quantisation
- The concept that a physical quantity can only have certain discrete values, rather than any continuous value.
Worked Examples
Worked Example
Question: In a photoelectric effect experiment, light of frequency 7.5 x 10¹⁴ Hz is shone on a metal surface with a work function of 2.1 eV. Calculate the maximum kinetic energy of the emitted photoelectrons, in Joules.
Solution: Step 1: Convert the work function from electron-volts (eV) to Joules (J). φ = 2.1 eV * (1.60 x 10⁻¹⁹ J/eV) = 3.36 x 10⁻¹⁹ J Step 2: Calculate the energy of the incident photons using E = hf. E = (6.63 x 10⁻³⁴ J s) * (7.5 x 10¹⁴ Hz) = 4.9725 x 10⁻¹⁹ J Step 3: Use the photoelectric equation to find the maximum kinetic energy. KE_max = hf - φ KE_max = 4.9725 x 10⁻¹⁹ J - 3.36 x 10⁻¹⁹ J Final answer: KE_max = 1.61 x 10⁻¹⁹ J (to 3 s.f.)
Worked Example
Question: A spaceship travels past the Earth at a speed of 0.80c. An astronaut on the spaceship measures the journey between two stars to take 5.0 years. Calculate the time for the journey as measured by an observer on Earth.
Solution: Step 1: Identify the proper time, t₀. The astronaut is on the spaceship and is present at both the start and end of the journey, so their measurement is the proper time. t₀ = 5.0 years Step 2: Calculate the Lorentz factor, γ. γ = 1 / √(1 - v²/c²) = 1 / √(1 - (0.80c)²/c²) = 1 / √(1 - 0.64) = 1 / √0.36 = 1 / 0.6 = 1.67 Step 3: Use the time dilation formula t = γt₀. t = 1.67 * 5.0 years Final answer: t = 8.35 years
Worked Example
Question: Explain how the observations of the photoelectric effect provide evidence for the particle nature of light and contradict the wave model.
Solution: Observation 1: Instantaneous emission of photoelectrons occurs if the frequency of light is above the threshold frequency. The wave model would predict a time delay, as energy would need to be absorbed by the electron over time before it had enough to escape. The particle model explains this as a single photon gives all its energy to a single electron in a one-to-one interaction, causing immediate emission. Observation 2: A threshold frequency exists below which no photoelectrons are emitted, regardless of the light's intensity. The wave model predicts that any frequency of light, if intense enough, should eventually provide enough energy for an electron to escape. The particle model explains this because each photon has energy E=hf, and if this is less than the work function, the electron cannot escape, no matter how many photons arrive. Observation 3: The maximum kinetic energy of the photoelectrons depends on the frequency of the light, not its intensity. The wave model predicts that higher intensity (more energy per second) should lead to higher kinetic energy. The particle model explains this as one photon interacts with one electron, so higher frequency photons (more energy per photon) give the electrons more kinetic energy after overcoming the work function. Higher intensity just means more photons, so more electrons are emitted, but their max KE is unchanged.
Practice Questions
Question: Describe the Michelson-Morley experiment and explain the significance of its null result.
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Question: An electron is accelerated from rest through a potential difference of 5.0 kV. Calculate its specific charge if it is then deflected into a circular path of radius 3.0 cm by a uniform magnetic field of flux density 3.2 mT applied perpendicular to its velocity.
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Question: A muon is an unstable particle that decays with a half-life of 2.2 μs in its own rest frame. A beam of muons is produced travelling at 0.99c. Calculate the half-life of the muons in the laboratory frame.
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Question: State two features of the photoelectric effect that cannot be explained by the wave theory of light.
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Question: A stationary oil droplet of mass 1.2 x 10⁻¹⁴ kg is held between two parallel plates 1.5 cm apart. The droplet has a charge equivalent to 5 electrons. Calculate the potential difference between the plates. You may ignore the effects of air buoyancy.
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