Modern Physics - Photoelectric Effect and Nuclear Physics Solved Examples (Class 12 Physics)
Modern physics numericals cover photoelectric effect, nuclear decay, and atomic phenomena. These problems introduce quantum concepts and nuclear structure
TL;DR: Modern physics numericals cover photoelectric effect, nuclear decay, and atomic phenomena. These problems introduce quantum concepts and nuclear struc…
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Modern physics numericals cover photoelectric effect, nuclear decay, and atomic phenomena. These problems introduce quantum concepts and nuclear structure
Modern Physics - Photoelectric Effect and Nuclear Physics — Solved Numerical Examples (Step by Step)
Example 1: Light of wavelength 250 nm hits a metal surface with work function 2 eV. Calculate kinetic energy of ejected electrons. (h = 6.63 × 10^-34 J·s, c = 3 × 10^8 m/s, 1 eV = 1.6 × 10^-19 J)
Solution: Wavelength λ = 250 × 10^-9 m, Work function W = 2 eV = 3.2 × 10^-19 J, h = 6.63 × 10^-34 J·s, c = 3 × 10^8 m/s. Energy of photon E = hc/λ = (6.63 × 10^-34 × 3 × 10^8) / (250 × 10^-9) = (1.989 × 10^-25) / (250 × 10^-9) = 7.956 × 10^-19 J = 4.97 eV. Kinetic energy = E - W = 4.97 - 2 = 2.97 eV.
Example 2: Calculate the threshold frequency for a metal with work function 3 eV. (h = 6.63 × 10^-34 J·s, 1 eV = 1.6 × 10^-19 J)
Solution: Work function W = 3 eV = 4.8 × 10^-19 J. Using W = h × f₀: f₀ = W/h = (4.8 × 10^-19) / (6.63 × 10^-34) = 7.24 × 10^14 Hz.
Example 3: A radioactive nucleus decays with half-life 10 days. What fraction remains after 30 days?
Solution: Half-life t₁/₂ = 10 days, Time elapsed t = 30 days. Number of half-lives n = t / t₁/₂ = 30 / 10 = 3. Fraction remaining = (1/2)^n = (1/2)³ = 1/8 = 0.125 = 12.5%.
Example 4: Calculate the nuclear binding energy of a nucleus if mass defect is 0.5 u. (1 u = 931.5 MeV/c²)
Solution: Mass defect Δm = 0.5 u. Binding energy BE = Δm × c² = 0.5 × 931.5 = 465.75 MeV.
Example 5: Find the activity of a radioactive sample with 10^20 atoms and decay constant 0.1 s^-1.
Solution: Number of atoms N = 10^20, Decay constant λ = 0.1 s^-1. Activity A = λ × N = 0.1 × 10^20 = 10^19 Bq.
Tips
- Photoelectric effect: KE = hf - W, where hf is photon energy and W is work function.
- Threshold frequency f₀ = W/h; light below this frequency cannot eject electrons.
- Radioactive decay: N(t) = N₀ × (1/2)^(t/t₁/₂).
Frequently Asked Questions
Why does increasing light intensity not eject more energetic electrons?
Kinetic energy of ejected electrons depends on light frequency (photon energy), not intensity. Intensity only increases the number of photons, ejecting more electrons but with same KE.
What is nuclear binding energy?
Binding energy is the energy required to disassemble a nucleus into separate nucleons. It represents the mass defect converted to energy via E = mc².
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