ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Electronics, Modern, Atomic and Nuclear Physics (Set 5): 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. Use hc = 1240 eV nm. Light of wavelength 310 nm falls on a metal of work function 2.0 eV. The stopping potential is:
Answer: A. 2.0 V
Explanation: Photon energy = 1240/310 = 4.0 eV. K_max = 4.0 − 2.0 = 2.0 eV, so the stopping potential is 2.0 V.
Q2. A metal has threshold frequency f₀. The maximum kinetic energy of photoelectrons when the metal is lit by light of frequency 2f₀ is K₁, and when lit by light of frequency 3f₀ is K₂. The ratio K₁ : K₂ is:
Answer: A. 1 : 2
Explanation: K = hf − hf₀. K₁ = hf₀ and K₂ = 2hf₀, so K₁ : K₂ = 1 : 2.
Q3. A laser emits 3 mW of light of wavelength 620 nm (take hc = 1240 eV nm and 1 eV = 1.6 × 10⁻¹⁹ J). The number of photons emitted per second is approximately:
Answer: A. 9.4 × 10¹⁵
Explanation: Photon energy = 1240/620 = 2 eV = 3.2 × 10⁻¹⁹ J. N = P/E = 3×10⁻³/3.2×10⁻¹⁹ ≈ 9.4 × 10¹⁵ s⁻¹.
Q4. An electron and a proton have the same kinetic energy. The ratio of the de Broglie wavelength of the electron to that of the proton (λ_e/λ_p) is approximately (m_p/m_e = 1836):
Answer: C. 43
Explanation: λ = h/√(2mK), so λ_e/λ_p = √(m_p/m_e) = √1836 ≈ 43.
Q5. The Compton wavelength of the electron is h/m_ec = 2.43 pm. The largest possible increase in wavelength of an X-ray photon scattered by a free electron is:
Answer: D. 4.86 pm
Explanation: Δλ = (h/m_ec)(1 − cosθ). It is greatest at θ = 180°, where (1 − cosθ) = 2: Δλ = 4.86 pm.
Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.
Q6. Muons have a proper mean lifetime of 2.2 μs. A beam of muons travels at 0.8c (c = 3 × 10⁸ m s⁻¹). The mean distance they travel in the laboratory before decaying is:
Q7. A rod is measured to be exactly half of its rest length by an observer moving along its length. The relative speed of the observer is:
Q8. The Sun radiates energy at about 3.6 × 10²⁶ W. Using E = mc² with c = 3 × 10⁸ m s⁻¹, the rate at which the Sun loses mass is approximately:
Q9. The rest energy of an electron is 0.511 MeV. Its kinetic energy when moving at 0.6c is approximately:
Q10. A gamma-ray photon of energy 3.022 MeV produces an electron–positron pair. Taking the rest energy of each particle as 0.511 MeV, the total kinetic energy shared by the pair is:
Q11. A spherical black body has radius r and absolute temperature T. If its radius is doubled and its temperature halved, the total power radiated changes by a factor of:
Q12. Let λ_L be the longest wavelength in the Lyman series and λ_B the longest wavelength in the Balmer series of hydrogen. The ratio λ_L : λ_B is:
Q13. In the Bohr model, the orbital period of an electron in the n = 3 orbit of hydrogen compared with its period in the n = 1 orbit is larger by a factor of:
Q14. A large number of hydrogen atoms are excited to the n = 4 level. The maximum number of different spectral lines that can be emitted as they return to lower levels is:
Q15. Treating a Li²⁺ ion (Z = 3, one electron) by the Bohr model, with 13.6 eV the ionisation energy of hydrogen, the energy needed to remove the electron from its ground state is:
Q16. In an X-ray tube operated at 31 kV, the shortest X-ray wavelength produced is approximately (hc = 1240 eV nm):
Q17. Which of the following is essential for laser action in a medium?
Q18. Nucleus X has a mass number of 64 and nucleus Y has a mass number of 8. The ratio of the radius of X to the radius of Y is:
Q19. A radioactive sample decays for a time equal to its mean life (the reciprocal of the decay constant). The fraction of the original nuclei that have decayed is about:
Q20. A uranium-238 nucleus (Z = 92) decays through a series of α and β⁻ emissions to a stable lead-206 nucleus (Z = 82). The number of α and β⁻ particles emitted is:
Q21. Atomic masses: ¹H = 1.007825 u, neutron = 1.008665 u, ²H = 2.014102 u (1 u = 931.5 MeV/c²). The binding energy per nucleon of the deuteron is approximately:
Q22. In the fusion reaction ²H + ³H → ⁴He + n, 17.6 MeV is released as kinetic energy of the products. Taking the initial momentum as zero and mass numbers as masses, the neutron's kinetic energy is about:
Q23. Each fission of a uranium-235 nucleus releases about 200 MeV (1 MeV = 1.6 × 10⁻¹³ J). Taking the molar mass as 235 g mol⁻¹ and N_A = 6 × 10²³ mol⁻¹, the energy released by fully fissioning 1 kg is approximately:
Q24. A silicon diode with a forward drop of 0.7 V is connected in series with a 100 Ω resistor and a 5.7 V battery, forward biased. The current in the circuit is:
Q25. An ideal full-wave rectifier is supplied from a 220 V rms, 50 Hz AC source (peak = 311 V). The mean (dc) output voltage is approximately:
Q26. In a transistor, the common-base current gain α is related to the common-emitter gain β by α = β/(1 + β). For a transistor with β = 49, α is:
Q27. An op-amp is connected as a non-inverting amplifier with a 2 kΩ resistor from the inverting input to ground and an 18 kΩ feedback resistor. An input signal of 0.4 V gives an output of:
Q28. The circuit output is Y = NOR(A AND B, C). For which set of inputs (A, B, C) is Y equal to 1?
Q29. An electron is confined within a region of size Δx = 0.1 nm. Using Δx Δp ≥ h/4π with h = 6.63 × 10⁻³⁴ J s and m = 9.1 × 10⁻³¹ kg, the minimum uncertainty in its speed is approximately:
Q30. A 6 W beam of light is reflected perfectly back along its path by a mirror (c = 3 × 10⁸ m s⁻¹). The force the light exerts on the mirror is: