NUMS — Medical & Dental Entry Test
Take the NUMS Physics — Electronics, Modern and Nuclear Physics (Set 6): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. A phototube is illuminated by 2.0 mW of light of wavelength 400 nm. Each 100 incident photons eject on average one photoelectron, and all the electrons are collected. What is the photocurrent? (h = 6.626 × 10⁻³⁴ J s, c = 3.0 × 10⁸ m s⁻¹, e = 1.602 × 10⁻¹⁹ C)
Answer: C. 6.4 µA
Explanation: Photon energy = hc/λ = 4.97 × 10⁻¹⁹ J. Photons per second = 2.0 × 10⁻³/4.97 × 10⁻¹⁹ = 4.02 × 10¹⁵. Electrons per second = 1% of that = 4.02 × 10¹³. I = 4.02 × 10¹³ × 1.602 × 10⁻¹⁹ = 6.4 × 10⁻⁶ A = 6.4 µA.
Q2. According to Bohr's model, how does the orbital period of the electron in the n = 2 orbit of hydrogen compare with that in the n = 1 orbit?
Answer: B. 8 times longer
Explanation: rₙ ∝ n² and vₙ ∝ 1/n, so T = 2πr/v ∝ n³. For n = 2 the period is 2³ = 8 times that for n = 1.
Q3. In Bohr's model the total energy of the electron in the ground state of hydrogen is −13.6 eV. What is its electrostatic potential energy in this state?
Answer: C. −27.2 eV
Explanation: For a circular Coulomb orbit, KE = −E_total = +13.6 eV and PE = 2E_total = −27.2 eV, so that the total is −27.2 + 13.6 = −13.6 eV.
Q4. A 2.00 MeV gamma-ray photon converts into an electron–positron pair near a nucleus. Taking the rest energy of each particle as 0.511 MeV and assuming the recoil of the nucleus is negligible and the kinetic energy is shared equally, what is the kinetic energy of each particle?
Answer: D. 0.49 MeV
Explanation: Energy available for kinetic energy = 2.00 − 2(0.511) = 0.978 MeV. Shared equally, each particle has 0.489 MeV ≈ 0.49 MeV.
Q5. What is the kinetic energy of an electron moving at 0.8c? (rest energy 0.511 MeV)
Answer: A. 0.34 MeV
Explanation: γ = 1/√(1 − 0.64) = 1/0.6 = 1.667; KE = (γ − 1) × 0.511 = 0.667 × 0.511 ≈ 0.34 MeV.
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Q6. A particle of rest mass m₀ moves at 0.60c. What is its relativistic kinetic energy?
Q7. A 5.0 MeV alpha particle is fired head-on at a gold nucleus (Z = 79). Treating the nucleus as a fixed point charge, what is the distance of closest approach? (k = 9.0 × 10⁹ N m² C⁻², e = 1.60 × 10⁻¹⁹ C)
Q8. How does the density of nuclear matter in a ²³⁸U nucleus compare with that in a ¹²C nucleus, given R = R₀A^(1/3)?
Q9. In Rutherford's first artificial transmutation, ¹⁴₇N was bombarded with alpha particles: ¹⁴₇N + ⁴₂He → ¹⁷₈O + X. What is X?
Q10. Uranium-235 (Z = 92) decays through a long series to stable lead-207 (Z = 82). How many α and β⁻ particles are emitted in total?
Q11. Two radioactive samples X (half-life 2 h) and Y (half-life 4 h) have equal activities at t = 0. What is the ratio of the activity of X to that of Y after 8 h?
Q12. The mean life of a radioactive nuclide is 20 s. What is its half-life?
Q13. A nuclide can decay by two independent routes: by α emission alone it would have a half-life of 40 years and by β emission alone a half-life of 60 years. What is its actual half-life?
Q14. A nucleus of mass number 240 (binding energy about 7.6 MeV per nucleon) splits into two equal fragments of mass number 120 (binding energy about 8.5 MeV per nucleon). Approximately how much energy is released?
Q15. A mineral sample contains ²³⁸U and its final decay product ²⁰⁶Pb in equal numbers of atoms, and it is assumed that no lead was present initially. If the half-life of ²³⁸U is 4.5 × 10⁹ years, what is the age of the mineral?
Q16. A neutron (mass 1 u) of energy 2.0 MeV makes a head-on elastic collision with a stationary carbon-12 nucleus (mass 12 u). What fraction of its kinetic energy does the neutron retain? (Use ((A − 1)/(A + 1))² for a head-on collision.)
Q17. Why do heavy stable nuclei contain more neutrons than protons?
Q18. A 5.1 V Zener diode has a maximum power rating of 500 mW. What is the maximum current it can safely carry in breakdown?
Q19. An inverting amplifier with a gain of −20 is built from an ideal op-amp powered from ±12 V supplies, and the input is 0.80 V. What is the output voltage? (Assume the output cannot exceed the supply rails.)
Q20. Which expression is equivalent to Y = A + Ā·B?
Q21. What is the decimal number 45 in binary?
Q22. A two-input NOR gate has both of its inputs connected together to a single signal A. What function does it perform?
Q23. Silicon (intrinsic carrier concentration nᵢ = 1.5 × 10¹⁶ m⁻³) is doped with phosphorus so that the electron concentration is 1.0 × 10²² m⁻³. Using n·p = nᵢ², what is the hole concentration?
Q24. A half-wave rectifier is fed from a transformer secondary giving 12 V rms. What is the peak inverse voltage that its diode must withstand (taking the ideal case with no smoothing capacitor)?
Q25. A full-wave rectifier (output ripple at 100 Hz) with a smoothing capacitor of 1000 µF supplies a steady load current of 0.10 A. Using the approximation ΔV = I/(fC), what is the peak-to-peak ripple voltage?
Q26. A red LED has a forward voltage drop of 2.0 V and is to carry 15 mA from a 5.0 V supply. What series resistor is needed?
Q27. For a transistor in common-base mode the current gain α = I_C/I_E is 0.98. What is the common-emitter current gain β = I_C/I_B?
Q28. A silicon diode (forward drop 0.7 V) is connected in forward bias in series with a 1.0 kΩ resistor across a 5.0 V battery. What current flows in the circuit?
Q29. A light-dependent resistor (LDR) is in series with a fixed 10 kΩ resistor across a 6.0 V supply. In bright light the LDR has a resistance of 1 kΩ. What is the voltage across the fixed resistor?
Q30. Which condition must be met for a transistor amplifier with feedback to sustain steady oscillations?