Chapter 12: Formula Reference — Modern Physics
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Modern physics covers phenomena that classical (Newtonian) mechanics could not fully explain, including the particle nature of light, the structure of the atom, radioactivity, and the equivalence of mass and energy established by Einstein's theory of relativity. This branch is a regular source of both formula-based and factual questions in SSC/RRB exams.
12.1 Photoelectric Effect and Quantum Physics
Quantity / Law | Formula | Symbols & SI Units |
|---|---|---|
Energy of a photon | E = hf = hc/λ | h = Planck's constant = 6.626 × 10⁻³⁴ J·s, f = frequency (Hz), c = speed of light, λ = wavelength (m) |
Einstein's Photoelectric Equation | Emax = hf − W₀ | Emax = maximum kinetic energy of emitted electron (J), W₀ = work function of the metal (J) |
Work function (threshold frequency) | W₀ = hf₀ | f₀ = threshold frequency, below which no photoelectric emission occurs regardless of intensity |
12.2 Mass–Energy Equivalence
Quantity / Law | Formula | Symbols & SI Units |
|---|---|---|
Einstein's Mass–Energy Relation | E = mc² | E = energy (J), m = mass (kg), c = speed of light in vacuum ≈ 3 × 10⁸ m/s |
12.3 Atomic Structure and Radioactivity
Quantity / Law | Formula / Statement | Notes |
|---|---|---|
Rutherford's model | Atom has a small, dense, positively charged nucleus with electrons orbiting around it | Based on the alpha-particle scattering experiment |
Bohr's model | Electrons revolve in fixed, quantised orbits without radiating energy | Explained the hydrogen spectrum |
Radioactive decay law | N = N₀e^(−λt) | N₀ = initial number of nuclei, N = number remaining after time t, λ = decay constant |
Half-life | t½ = 0.693/λ | Time taken for half of a radioactive sample to decay |
Alpha decay | Emission of a helium nucleus (2 protons + 2 neutrons); mass number decreases by 4, atomic number decreases by 2 | Alpha particles have the least penetrating power but highest ionising power among α, β, γ |
Beta decay | Emission of an electron (or positron); atomic number changes by 1, mass number unchanged | Beta particles have intermediate penetrating power |
Gamma decay | Emission of high-energy electromagnetic radiation (photons); no change in mass number or atomic number | Gamma rays have the highest penetrating power but lowest ionising power |
12.4 Fundamental Physical Constants — Quick Reference
Constant | Symbol | Approximate Value |
|---|---|---|
Speed of light in vacuum | c | 3 × 10⁸ m/s (exactly 299,792,458 m/s) |
Planck's constant | h | 6.626 × 10⁻³⁴ J·s |
Charge of an electron (elementary charge) | e | 1.602 × 10⁻¹⁹ C |
Mass of an electron | mₑ | 9.11 × 10⁻³¹ kg |
Mass of a proton | mₚ | 1.673 × 10⁻²⁷ kg |
Avogadro constant | NA | 6.022 × 10²³ per mole |
Universal gravitational constant | G | 6.674 × 10⁻¹¹ N·m²/kg² |
Boltzmann constant | k | 1.381 × 10⁻²³ J/K |
Universal gas constant | R | 8.314 J/(mol·K) |
Permittivity of free space | ε₀ | 8.854 × 10⁻¹² C²/(N·m²) |
Permeability of free space | μ₀ | 4π × 10⁻⁷ T·m/A |
Standard acceleration due to gravity | g | 9.8 m/s² (approx.; standard value 9.80665 m/s²) |