ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Electronics, Modern, Atomic and Nuclear Physics (Set 4): 30 multiple-choice questions (40 minutes) with instant scoring and a full…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. Light of photon energy 4.0 eV gives a stopping potential of 2.0 V in a photoelectric experiment. If the frequency of the light is doubled, the stopping potential becomes
Answer: A. 6.0 V
Explanation: φ = 4.0 − 2.0 = 2.0 eV. At double frequency the photon energy is 8.0 eV, so eV_s = 8.0 − 2.0 = 6.0 eV and V_s = 6.0 V.
Q2. A metal has a work function of 2.48 eV. Taking hc = 1240 eV nm, its threshold wavelength is
Answer: A. 500 nm
Explanation: λ₀ = hc/φ = 1240/2.48 = 500 nm.
Q3. A source emits monochromatic light of wavelength 496 nm with power 2 mW. Taking hc = 1240 eV nm and e = 1.6 × 10⁻¹⁹ C, the number of photons emitted per second is
Answer: A. 5 × 10¹⁵
Explanation: E = 1240/496 = 2.5 eV = 4 × 10⁻¹⁹ J. N = P/E = (2 × 10⁻³)/(4 × 10⁻¹⁹) = 5 × 10¹⁵ s⁻¹.
Q4. An electron accelerated through 150 V has a de Broglie wavelength (use λ = 1.227/√V nm, V in volts) of about
Answer: B. 0.10 nm
Explanation: λ = 1.227/√150 = 1.227/12.25 ≈ 0.100 nm.
Q5. An electron and a proton have equal kinetic energies. The ratio of the electron's de Broglie wavelength to the proton's is about (m_p/m_e = 1836)
Answer: D. 43
Explanation: λ = h/√(2mK) ∝ 1/√m, so λ_e/λ_p = √(m_p/m_e) = √1836 ≈ 43.
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Q6. The energy of the n = 2 level of the doubly ionised lithium ion Li²⁺ (Z = 3), given that the hydrogen ground state is −13.6 eV, is
Q7. In the Bohr model of hydrogen, the ratio of the orbital period of the electron in the n = 3 orbit to that in the n = 1 orbit is
Q8. The longest wavelength in the Paschen series of hydrogen (R = 1.097 × 10⁷ m⁻¹) is about
Q9. The activity of a radioactive sample falls from 1600 Bq to 200 Bq in 3 hours. Its half-life is
Q10. A radioactive isotope has a half-life of 10 days. Its mean life is about
Q11. A uranium-238 nucleus (Z = 92) ends as stable lead-206 (Z = 82) after a series of decays. The numbers of α and β⁻ particles emitted are
Q12. Sample A has a half-life of 1 hour and sample B a half-life of 2 hours. They start with equal numbers of nuclei. After 4 hours the ratio of the number of undecayed nuclei in A to that in B is
Q13. The Sun radiates about 4 × 10²⁶ W. Taking c = 3 × 10⁸ m/s, the rate at which it loses mass is about
Q14. The mass defect of a helium-4 nucleus is 0.0304 u (1 u = 931.5 MeV/c²). The binding energy per nucleon is about
Q15. If each fission of a U-235 nucleus releases 200 MeV, the energy released by the complete fission of 1 kg of U-235 (take N_A = 6.02 × 10²³ per mole, 1 MeV = 1.6 × 10⁻¹³ J) is about
Q16. Taking the nuclear radius as R = R₀A^(1/3) with R₀ = 1.2 fm, the radius of an aluminium-27 nucleus is
Q17. Muons have a proper mean lifetime of 2.2 μs. For muons travelling at 0.8c (c = 3 × 10⁸ m/s), the average distance covered before decaying, as measured in the laboratory, is
Q18. A spaceship of proper length 100 m passes an observer and is measured to be 60 m long. Its speed is
Q19. A particle moves at 0.6c. Its kinetic energy as a fraction of its rest energy is
Q20. An electron and a positron annihilate at rest producing two identical photons. Taking the electron rest energy as 0.511 MeV and hc = 1240 eV nm, the wavelength of each photon is about
Q21. For Compton scattering from free electrons, given that h/mc = 2.43 pm, the largest possible change in wavelength of the scattered photon is
Q22. The accelerating voltage of an X-ray tube is 31 kV. Taking hc = 1240 eV nm, the minimum wavelength of the X-rays emitted is
Q23. In a transistor with current gain β = 100 (common emitter), the base current is 40 μA. The emitter current is
Q24. A non-inverting op-amp amplifier has a feedback resistor of 90 kΩ and an input resistor of 10 kΩ to ground. For an input of 0.25 V the output voltage is
Q25. A two-input NOR gate has both of its inputs connected together to a single input A. The gate then behaves as a
Q26. A logic circuit gives Y = (A · B) + (A · B̄), where B̄ is NOT B. The output Y equals
Q27. The small current that flows in a reverse-biased p–n junction diode is due to
Q28. The absolute temperature of a black body is increased from 300 K to 900 K. The rate at which it radiates energy increases by a factor of
Q29. Which condition is essential for laser action to take place in a medium?
Q30. A full-wave rectifier using two diodes is fed from 50 Hz mains through a centre-tapped transformer. The fundamental frequency of the ripple in its output is