Modern Physics

1. Photoelectric Effect

• When light shines on a metal surface, electrons can be ejected — but only if the light's photon energy exceeds the metal's work function φ (the minimum energy needed to free an electron).
• Maximum kinetic energy of ejected electrons: KE_max = E_photon − φ, where E_photon = hf (h = Planck's constant, f = light frequency).
• Threshold frequency: the minimum frequency at which photoelectrons are emitted at all, where E_photon = φ exactly (KE_max = 0).
• Below the threshold frequency, NO electrons are emitted no matter how intense the light is — intensity only affects the NUMBER of electrons emitted (once above threshold), not their maximum energy.

Common mistakes: thinking brighter (more intense) light always ejects more energetic electrons — intensity affects electron COUNT, not their max kinetic energy; forgetting KE_max can never be negative — if E_photon < φ, no electrons are emitted at all (not "negative energy" electrons).

2. Atomic Structure

• The (simplified) Bohr model: electrons orbit the nucleus only in specific allowed energy levels; they don't lose energy while in a stable orbit.
• Electrons can jump between energy levels by absorbing a photon (moving to a higher level) or emitting a photon (dropping to a lower level).
• The photon's energy exactly equals the energy difference between the two levels: E_photon = E_high − E_low.

Common mistakes: thinking electrons can occupy any energy level (they can only occupy specific quantized levels); confusing absorption (jumping up, needs incoming photon) with emission (dropping down, releases a photon).

3. Nuclear Physics — Basics

• An isotope is a version of an element with the same number of protons but a different number of neutrons.
• Radioactive decay types: alpha decay (emits a helium nucleus, 2 protons + 2 neutrons — mass number drops by 4, atomic number drops by 2), beta decay (a neutron converts to a proton, emitting an electron — atomic number increases by 1, mass number unchanged), gamma decay (emits high-energy photons, no change in mass or atomic number).
• Half-life: the time for half of a radioactive sample to decay. After n half-lives, the remaining fraction is (1/2)ⁿ.

Common mistakes: forgetting alpha decay changes BOTH mass number (−4) and atomic number (−2), while beta decay only changes atomic number (+1) and leaves mass number unchanged; miscalculating half-life problems by using n×(half-life) as a simple fraction instead of (1/2)ⁿ.