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Quantum Physics and Nuclear Physics

Subject: Physics
Topic: 8
Cambridge Code: 0625

Photons and Light Energy​

Photon - Discrete energy packet of light

Energy of Photon​

E=hf=hcλE = hf = \frac{hc}{λ}

Where:

  • h = Planck's constant = 6.63 × 10⁻³⁴ J·s
  • f = frequency
  • c = speed of light = 3 × 10⁸ m/s
  • λ = wavelength

Higher frequency → more energy

Momentum of Photon​

p=Ec=hfc=hλp = \frac{E}{c} = \frac{hf}{c} = \frac{h}{λ}

Work Function and Photoelectric Effect​

Photoelectric effect - Electrons released from metal by light

Work Function (Φ)​

Minimum energy needed to remove electron:

E=hf0=ΦE = hf_0 = Φ

Where f0f_0 is threshold frequency

For frequency above threshold: hf=Φ+Ekhf = Φ + E_k

Einstein's photoelectric equation: hf=Φ+12mvmax2hf = Φ + \frac{1}{2}mv_{\text{max}}^2

Key Points​

Photons below threshold:

  • No electrons released (regardless of intensity)

Photons above threshold:

  • Electrons released with kinetic energy
  • More intense light → more electrons (not faster)
  • Higher frequency → faster electrons

Stopping potential (V_s): eVs=12mvmax2eV_s = \frac{1}{2}mv_{\text{max}}^2

Energy Levels​

Energy levels - Discrete energies allowed for electrons

Excitation and Deexcitation​

Electron absorbs photon:

  • Jumps to higher level
  • hf=E2−E1hf = E_2 - E_1 (difference between levels)

Electron falls to lower level:

  • Emits photon
  • hf=E2−E1hf = E_2 - E_1

Spectral lines correspond to:

  • Different energy level transitions
  • Absorbed or emitted light

Ionization​

Energy needed to remove electron completely:

Ionization energy=hf\text{Ionization energy} = hf

Where f is frequency of ionizing radiation

Atomic Spectra​

Emission spectrum:

  • Bright lines on dark background
  • Specific wavelengths from excited atoms

Absorption spectrum:

  • Dark lines on bright background
  • Wavelengths absorbed by atoms

Spectral lines unique to each element - Used for identification

Nuclear Structure​

Nucleus contains:

  • Protons: Positive charge, mass ≈ 1 u
  • Neutrons: No charge, mass ≈ 1 u

Electrons orbit nucleus: Negative charge, much smaller mass

Notation​

ZAX{}^A_Z\text{X}

Where:

  • X = element symbol
  • A = mass number (protons + neutrons)
  • Z = atomic number (protons)

Neutron number (N) = A - Z

Isotopes​

Atoms of same element (same Z, different A)

  • Different neutrons
  • Different mass
  • Chemical behavior same
  • Radioactivity different

Radioactivity​

Radioactivity - Spontaneous nuclear decay

Types of Decay​

Alpha decay (α): Emits helium nucleus 24He{}^4_2\text{He} ZAX→Z−2A−4Y+24He{}^A_Z\text{X} → {}^{A-4}_{Z-2}\text{Y} + {}^4_2\text{He}

Beta-minus decay (β⁻): Neutron → proton + electron ZAX→Z+1AY+−10e{}^A_Z\text{X} → {}^A_{Z+1}\text{Y} + {}^0_{-1}\text{e}

Beta-plus decay (β⁺): Proton → neutron + positron

Gamma decay (γ): Emits high-energy photon

  • Mass number A unchanged
  • Atomic number Z unchanged

Activity and Half-Life​

Activity (A) - Number of decays per second

A=λNA = λN

Where:

  • λ = decay constant
  • N = number of nuclei remaining

Unit: Becquerels (Bq) = 1 decay/second

Half-Life​

Half-life (t1/2t_{1/2}) - Time for half the nuclei to decay

N=N0(12)nN = N_0\left(\frac{1}{2}\right)^{n}

Where n = number of half-lives

Or exponentially: N=N0e−λtN = N_0e^{-λt}

Decay Curve​

Exponential decay:

  • Never reaches zero
  • Constant half-life
  • Log plot gives straight line

Mass-Energy Equivalence​

Einstein's Mass-Energy Relation:

E=mc2E = mc^2

Where:

  • E = energy
  • m = mass
  • c = speed of light

Application:

  • Matter can convert to energy
  • Energy can create mass
  • Nuclear reactions release large energy

Nuclear Binding Energy​

Mass defect: Loss of mass in nucleus

Δm=(Zmp+Nmn)−mnucleusΔm = (Zm_p + Nm_n) - m_{\text{nucleus}}

Binding energy: BE=Δmc2BE = Δmc^2

Energy required to break nucleus apart

Binding energy per nucleon: BEA\frac{BE}{A}

  • Higher = more stable nucleus
  • Peak at iron-56

Nuclear Fission and Fusion​

Fission​

Heavy nucleus splits into lighter nuclei

  • Releases neutrons (causes chain reaction)
  • Releases enormous energy
  • Used in nuclear reactors and bombs

Chain reaction: 1 neutron → 2 → 4 → 8 ...

Fusion​

Light nuclei combine to form heavier nucleus

  • Occurs at extreme temperature and pressure
  • Releases enormous energy
  • Sun's power source
  • Future clean energy source (hoped)

Background Radiation​

Natural radioactivity from environment:

Sources:

  • Radon gas (largest contributor)
  • Cosmic rays
  • Soil and rocks
  • Food and water
  • Medical procedures

Safety: Cumulative exposure should be minimized

Key Points​

  1. Photon energy E = hf
  2. Photoelectric effect needs photons above threshold
  3. Work function = minimum energy to remove electron
  4. Energy levels are discrete
  5. Spectral lines from level transitions
  6. Nucleus: protons + neutrons
  7. Isotopes: same Z, different A
  8. Radioactive decay: α, β, γ
  9. Half-life constant for each isotope
  10. E = mc² relates mass and energy

Practice Questions​

  1. Calculate photon energy
  2. Identify photoelectric effect
  3. Find threshold frequency
  4. Calculate stopping potential
  5. Interpret spectral lines
  6. Balance nuclear equations
  7. Identify decay types
  8. Calculate half-lives
  9. Determine remaining nuclei
  10. Calculate binding energy

Revision Tips​

  • Know E = hf thoroughly
  • Understand photoelectric concept
  • Learn decay equations
  • Practice half-life calculations
  • Know energy level transitions
  • Understand E = mc²
  • Know types of radiation
  • Practice nuclear equations
  • Consider practical applications