Introduction to Modern Physics

Classical physics (Newton's mechanics, Maxwell's electromagnetism) works wonderfully for everyday objects. But at the atomic scale, strange new rules take over. Modern physics -- born in the early 1900s -- revolutionized our understanding of atoms, light, and the universe.

The Photoelectric Effect

When light shines on certain metals, electrons are emitted. This is the photoelectric effect, explained by Einstein in 1905.

Key findings that classical physics could not explain:

• Below a certain threshold frequency, no electrons are emitted regardless of light intensity
• Kinetic energy of emitted electrons depends on frequency, not intensity

Einstein's equation: E = hf = phi + KE_max

where h = 6.63 x 10⁻³⁴ J s (Planck's constant), f is frequency, phi is the work function (minimum energy to release an electron), and KE_max is the maximum kinetic energy of emitted electrons.

Bohr's Model of the Atom

Niels Bohr proposed a model for the hydrogen atom with key postulates:

1. Electrons orbit the nucleus in specific allowed orbits without radiating energy
2. Angular momentum is quantized: L = n h/(2 pi), where n = 1, 2, 3, ...
3. Electrons emit or absorb photons when jumping between orbits

Energy of nth orbit: En = -13.6/n² eV (for hydrogen)

Radius of nth orbit: rn = 0.053 n² nm (for hydrogen)

Worked Example

Find the energy of a photon of light with frequency 5 x 10¹⁴ Hz.

Solution:

• E = hf = 6.63 x 10⁻³⁴ x 5 x 10¹⁴
• E = 3.315 x 10⁻¹⁹ J
• In eV: E = 3.315 x 10⁻¹⁹ / 1.6 x 10⁻¹⁹ = 2.07 eV

Nuclear Physics Basics

The nucleus contains protons (positive) and neutrons (neutral), held together by the strong nuclear force.

• Atomic number (Z): Number of protons
• Mass number (A): Total protons + neutrons
• Isotopes: Same Z, different A (e.g., Carbon-12 and Carbon-14)

Radioactivity

Unstable nuclei spontaneously emit radiation to become more stable. Three types:

• Alpha decay: Emits helium nucleus (2 protons + 2 neutrons). Least penetrating.
• Beta decay: Emits electron or positron. Moderate penetration.
• Gamma decay: Emits high-energy photon. Most penetrating.

Half-life: N = N0 (1/2)^(t/T_half)

Nepal Connection

Carbon-14 dating (a nuclear physics application) has been used to date archaeological findings in the Kathmandu Valley, helping establish the timeline of ancient Nepali civilization.

Key Takeaways

• Light behaves as particles (photons) in the photoelectric effect: E = hf
• Bohr model explains hydrogen's energy levels: En = -13.6/n² eV
• Radioactivity involves alpha, beta, and gamma emissions
• Half-life describes the rate of radioactive decay