Physics Practice Test: Modern Physics Basics

E = hf = (6.63 × 10⁻³⁴)(5.0 × 10¹⁴) ≈ 3.3 × 10⁻¹⁹ J. 1.3 × 10⁻⁴⁸ J divides h by f instead of multiplying.

Each electron absorbs one photon, and below the threshold no single photon has enough energy to free it. Brighter light means more photons, not more energetic ones; this result led Einstein to the photon idea.

KE_max = hf − φ = 4.0 − 2.5 = 1.5 eV. 6.5 eV adds the work function, but that energy is used up freeing the electron.

15 days is three half-lives: 80 → 40 → 20 → 10 g. 26.7 g divides by 3, as if the decay were linear.

An alpha particle is a helium-4 nucleus, so the mass number drops by 4 (226 → 222) and the atomic number by 2 (88 → 86). The new element is radon.

In beta-minus decay a neutron becomes a proton, so the atomic number rises by 1 while the mass number stays the same. Losing two protons and two neutrons is alpha decay.

E = mc² = (1.0 × 10⁻³ kg)(3.0 × 10⁸)² = 9.0 × 10¹³ J. 9.0 × 10¹⁶ J uses 1 kg instead of 1 g.

ΔE = 13.6(1/4 − 1/9) ≈ 1.9 eV, which is red light. 12.1 eV is the drop from n = 3 to n = 1, and 3.4 eV and 1.5 eV are just the energies of the single levels n = 2 and n = 3.

Gamma rays are high-energy photons with no charge, so they interact weakly with matter. Alpha particles are stopped by a sheet of paper, and beta particles by a few millimeters of aluminum.

This is time dilation: a moving clock is measured to tick slower by the factor γ, here 1/√(1 − 0.8²) ≈ 1.67. The astronauts notice nothing unusual about their own clock.