Dow University MDCAT / Entry Test Physics Modern Physics — Set 3

Dow University MDCAT / Entry Test Physics Modern Physics — Set 3

1. Question 1

   Q1. A photon with wavelength λ collides with an electron at rest. What formula governs the change in photon wavelength after scattering?

   • A) Δλ = h/(mc)(1 - cosθ)
   • B) Δλ = h/(mc)(1 + cosθ)
   • C) Δλ = 2h/(mc)
   • D) Δλ = h²/(mcλ)

   Answer: Δλ = h/(mc)(1 - cosθ)

   Explanation: Compton effect formula uses (1 - cosθ). Option B incorrectly adds cosθ.

2. Question 2

   Q2. An electron is accelerated through 100 V. What formula calculates its de Broglie wavelength?

   • A) λ = h/(√(2meV))
   • B) λ = h/(mv)
   • C) λ = h/(mc)
   • D) λ = hc/V

   Answer: λ = h/(√(2meV))

   Explanation: Relativistic acceleration uses √(2meV). Option B assumes classical velocity.

3. Question 3

   Q3. The half-life of a radioactive isotope is 10 days. What is its decay constant?

   • A) 0.0693 day⁻¹
   • B) 0.10 day⁻¹
   • C) 1.44 day⁻¹
   • D) 10 day⁻¹

   Answer: 0.0693 day⁻¹

   Explanation: λ = ln(2)/T½ ≈ 0.0693. Option B ignores natural log.

4. Question 4

   Q4. A nucleus has binding energy 8 MeV per nucleon. What formula gives total binding energy?

   • A) E = (Δm)c²
   • B) E = (Z + N) × 8 MeV
   • C) E = Z × 8 MeV
   • D) E = N × 8 MeV

   Answer: E = (Δm)c²

   Explanation: Mass-energy equivalence is universal. Option B misuses nucleon count.

5. Question 5

   Q5. In nuclear fission, 0.1% mass is converted to energy. What formula calculates energy released?

   • A) E = Δmc²
   • B) E = mc²/2
   • C) E = 0.1m × c
   • D) E = mc² × 0.1%

   Answer: E = Δmc²

   Explanation: Einstein's formula directly relates mass loss to energy. Option D ignores c².

6. Question 6

   Q6. A sample of 1000 atoms decays to 250 in 12 hours. What is its half-life?

   • A) 4 hours
   • B) 6 hours
   • C) 8 hours
   • D) 12 hours

   Answer: 6 hours

   Explanation: Decays by 1/4 in 12 hours → 2 half-lives. Option C ignores exponent.

7. Question 7

   Q7. A nucleus emits a photon with energy 5 MeV. What formula gives mass defect?

   • A) Δm = E/(c²)
   • B) Δm = E/c
   • C) Δm = Ec²
   • D) Δm = E²/c

   Answer: Δm = E/(c²)

   Explanation: Mass defect is energy divided by c². Option B misses c denominator.

8. Question 8

   Q8. A particle's position is measured with uncertainty Δx. What formula bounds its momentum uncertainty?

   • A) Δp ≥ ħ/(2Δx)
   • B) Δp ≥ ħ/Δx
   • C) Δp ≥ 2ħ/Δx
   • D) Δp ≥ ħ²/Δx

   Answer: Δp ≥ ħ/(2Δx)

   Explanation: Heisenberg's principle uses ħ/2. Option B doubles the threshold.

9. Question 9

   Q9. What minimum photon energy is required for pair production?

   • A) 1.02 MeV
   • B) 0.51 MeV
   • C) 1.53 MeV
   • D) 2.04 MeV

   Answer: 1.02 MeV

   Explanation: Pair production needs 2mc² (2×0.51 MeV). Option B is single electron mass.

10. Question 10

    Q10. Carbon-14 has a half-life of 5730 years. What formula calculates age of a sample with 25% remaining?

    • A) t = 2 × 5730
    • B) t = 5730 × ln(25)/ln(50)
    • C) t = 5730 × log(25)
    • D) t = 5730 × 4

    Answer: t = 2 × 5730

    Explanation: 25% remains after 2 half-lives. Option B uses incorrect logarithm.

11. Question 11

    Q11. An X-ray tube produces Kα radiation. What formula relates photon energy to atomic number?

    • A) E = 13.6(Z - 1)² eV
    • B) E = 13.6Z²/2
    • C) E = 13.6Z²
    • D) E = 13.6(Z - 2)²

    Answer: E = 13.6(Z - 1)² eV

    Explanation: Moseley's law uses (Z - 1)² for Kα. Option D subtracts 2 instead.

12. Question 12

    Q12. Photoelectrons are stopped by 3 V potential. What formula gives photon frequency?

    • A) f = (eV + Φ)/h
    • B) f = (eV - Φ)/h
    • C) f = eV/h
    • D) f = Φ/h

    Answer: f = (eV + Φ)/h

    Explanation: Work function must be overcome first. Option B subtracts Φ instead.

13. Question 13

    Q13. A nucleus has 60 neutrons and 45 protons. What is its N/Z ratio?

    • A) 1.33
    • B) 0.75
    • C) 1.50
    • D) 2.00

    Answer: 1.33

    Explanation: N/Z = 60/45 = 1.33. Option B swaps numerator/denominator.

14. Question 14

    Q14. In β⁻ decay, which particle is emitted alongside an electron?

    • A) Neutrino
    • B) Antineutrino
    • C) Positron
    • D) Gamma photon

    Answer: Antineutrino

    Explanation: Antineutrino conserves lepton number. Option A is for β⁺ decay.

15. Question 15

    Q15. A photon of wavelength 0.1 nm collides with an electron at rest. If the scattering angle is 60°, what is the change in wavelength? Use λ' - λ = (h/m_e c)(1 - cosθ)

    • A) 2.43 pm
    • B) 1.22 pm
    • C) 3.64 pm
    • D) 4.86 pm

    Answer: 1.22 pm

    Explanation: Compton shift formula gives 1.22 pm. Option D doubles the correct value.

16. Question 16

    Q16. An electron moving at 2 × 10⁶ m/s has a de Broglie wavelength of... (h = 6.63 × 10⁻³⁴ J·s, m_e = 9.11 × 10⁻³¹ kg)

    • A) 3.64 nm
    • B) 0.364 nm
    • C) 3.64 pm
    • D) 0.364 pm

    Answer: 3.64 nm

    Explanation: λ = h/(mv) = 3.64 nm. Option B divides by 1000 incorrectly.

17. Question 17

    Q17. Relativistic mass of a particle moving at 0.8c is... (m₀ = rest mass)

    • A) 1.67m₀
    • B) 0.6m₀
    • C) 1.25m₀
    • D) 2.5m₀

    Answer: 1.67m₀

    Explanation: m = m₀/√(1 - v²/c²) = 1.67m₀. Option C uses 0.6 instead of 1.67.

18. Question 18

    Q18. Binding energy of a nucleus with mass defect Δm = 0.02 u is... (1 u = 931.5 MeV/c²)

    • A) 18.63 MeV
    • B) 186.3 MeV
    • C) 9.315 MeV
    • D) 1.863 MeV

    Answer: 18.63 MeV

    Explanation: E = Δm × 931.5 = 18.63 MeV. Option B multiplies by 1000 unnecessarily.

19. Question 19

    Q19. Uncertainty in position Δx = 1 nm for a particle. Minimum Δp is... (h = 6.63 × 10⁻³⁴ J·s)

    • A) 5.28 × 10⁻²⁶ kg·m/s
    • B) 5.28 × 10⁻²⁹ kg·m/s
    • C) 1.06 × 10⁻²⁶ kg·m/s
    • D) 1.06 × 10⁻²³ kg·m/s

    Answer: 5.28 × 10⁻²⁶ kg·m/s

    Explanation: Δp ≥ h/(4πΔx) = 5.28 × 10⁻²⁶ kg·m/s. Option B divides by 1000 incorrectly.

20. Question 20

    Q20. Energy released in fusion of ²¹H + ³¹H → ⁴²He + n is... (Q = 17.6 MeV)

    • A) 17.6 MeV
    • B) 35.2 MeV
    • C) 8.8 MeV
    • D) 2.2 MeV

    Answer: 17.6 MeV

    Explanation: Q-value is directly given as 17.6 MeV. Option B doubles the correct value.