Modern Physics — Problem set, Grade 12

Compare wave–particle evidence, relativistic limits, and nuclear mass-energy accounting.

Review the key ideas

Photons, Photoelectric Effect & Wave–Particle Models

Photon frequency controls energy; intensity controls photon count at a fixed frequency.

Relativity, Light Speed & Model Limits

Near light speed, frame-dependent time, length, momentum, and energy extend everyday mechanics.

Mass–Energy, Nuclear Reactions & Radiation Evidence

Nuclear energy release follows total energy conservation and a consistently calculated rest-mass difference.

Problem 1

A photon has a frequency of 4 × 10¹⁴ Hz. Using h = 6.63 × 10⁻³⁴ J·s, find its energy.
Answer and explanation

About 2.65 × 10⁻¹⁹ J

E = h f = (6.63 × 10⁻³⁴) × (4 × 10¹⁴) = 26.52 × 10⁻²⁰ = 2.652 × 10⁻¹⁹ J.

Problem 2

Using hc=1240 eV·nm, find energy at 400 nm.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

3.1 eV

1240/400=3.1.

Problem 3

Which observation supports a wave model and which supports a photon model?
Answer and explanation

Interference supports wave superposition; threshold-dependent photoemission supports quantized energy exchange.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 4

Chapter review: A material has work function2.2 eV. Photons carry3.7 eV. Find Kmax in eV and joules, and stopping-potential magnitude.
Answer and explanation

Kmax=1.5 eV=2.403×10⁻¹⁹ J; stopping-potential magnitude=1.5 V. At fixed photon energy, increasing intensity changes available electron number rather than this maximum.

Kmax=1.5 eV=2.403×10⁻¹⁹ J; stopping-potential magnitude=1.5 V.

At fixed photon energy, increasing intensity changes available electron number rather than this maximum.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 5

Rest length 10 m,γ=1.25. Find length along motion.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

8 m

10/1.25=8.

Problem 6

Does a photon’s zero rest mass mean zero energy?
Answer and explanation

No. Its energy is hf and its momentum E/c.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 7

Chapter review: A process has proper duration3.0 μs and moves at0.80c relative to a lab. Find γ and lab duration; a rest10 m object moving parallel at that speed has what lab length?
Answer and explanation

γ=1/√0.36=5/3. Lab duration=5.0 μs; length=10/(5/3)=6.0 m, with simultaneous endpoints in the lab.

γ=1/√0.36=5/3.

Lab duration=5.0 μs; length=10/(5/3)=6.0 m, with simultaneous endpoints in the lab.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 8

Sample counts 80/min, background 20/min. Find net rate.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

60 counts/min

80−20=60.

Problem 9

Does rest-mass reduction violate energy conservation?
Answer and explanation

No; the difference appears as other forms of energy, with total energy conserved.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 10

Chapter review: A supplied reaction releases0.0015 u of rest-mass equivalent per event. Estimate energy in MeV, then explain why a detector count rate cannot directly give absorbed dose.
Answer and explanation

Energy≈0.0015×931.5=1.397 MeV/event. Dose also needs energy deposited, exposed mass, radiation characteristics and geometry; count rate includes detector efficiency/background and is not dose.

Energy≈0.0015×931.5=1.397 MeV/event.

Dose also needs energy deposited, exposed mass, radiation characteristics and geometry; count rate includes detector efficiency/background and is not dose.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.
Take the chapter quiz

Browse all courses