ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Electronics, Modern, Atomic and Nuclear Physics (Set 6): 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. A metal has a work function of 2.48 eV. Using hc = 1240 eV nm, the longest wavelength of light that can cause photoelectric emission from it is
Answer: A. 500 nm
Explanation: λ₀ = hc/φ = 1240/2.48 = 500 nm.
Q2. In a photoelectric experiment with light above the threshold frequency, the intensity of the light is doubled while its frequency is kept the same. Which statement is correct?
Answer: C. The saturation current doubles and the stopping potential is unchanged
Explanation: Intensity sets the number of photons (and so of photoelectrons) per second, which doubles the saturation current; each photon's energy hf is unchanged, so the maximum KE and stopping potential are unchanged.
Q3. In Compton scattering the shift in wavelength is Δλ = (h/m_ec)(1 − cosθ), with h/m_ec = 2.43 pm. The largest possible shift in the wavelength of the scattered photon is
Answer: A. 4.86 pm
Explanation: The shift is largest for backscattering (θ = 180°, cosθ = −1): Δλ = 2×2.43 = 4.86 pm.
Q4. An electron and a proton have the same kinetic energy. Take the proton to be 1600 times as massive as the electron. The ratio of the electron's de Broglie wavelength to the proton's is
Answer: D. 40
Explanation: λ = h/√(2mK) ∝ 1/√m, so λ_e/λ_p = √1600 = 40.
Q5. A laser beam of power 3.0 W strikes a mirror at normal incidence and is completely reflected (c = 3.0×10⁸ m/s). The force exerted on the mirror is
Answer: C. 2×10⁻⁸ N
Explanation: Photon momentum flow = P/c = 10⁻⁸ N. Reflection reverses it, doubling the momentum change: F = 2P/c = 2×10⁻⁸ N.
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Q6. The energy levels of a hydrogen-like ion of atomic number Z are Eₙ = −13.6Z²/n² eV. The energy of the photon emitted when He⁺ (Z = 2) falls from n = 2 to n = 1 is
Q7. Using a Rydberg constant of 1.0×10⁷ m⁻¹, the wavelength of the first line (n = 4 to n = 3) of the Paschen series of hydrogen is
Q8. The activity of a radioactive sample falls from 3200 counts per second to 100 counts per second in 40 minutes. Its half-life is
Q9. A radioisotope has a half-life of 10 days. Taking ln 2 = 0.693, its mean life is
Q10. Samples A and B start with equal numbers of radioactive atoms; their half-lives are 2 h and 4 h respectively. After 8 h the ratio of the activity of A to the activity of B is
Q11. The nuclear masses of the proton, neutron and helium-4 nucleus are 1.0073 u, 1.0087 u and 4.0015 u. Taking 1 u = 931.5 MeV/c², the binding energy per nucleon of helium-4 is
Q12. A reactor produces 100 MW of power from fission, each fission releasing 200 MeV (1 MeV = 1.6×10⁻¹³ J). The number of fissions per second is
Q13. In the fusion reaction ²H + ³H → ⁴He + n, the nuclear masses are 2.0141 u, 3.0160 u, 4.0026 u and 1.0087 u respectively. With 1 u = 931.5 MeV/c², the energy released is
Q14. A gamma-ray photon can create an electron–positron pair (rest energy of each 0.511 MeV). Using hc = 1240 MeV fm, the longest wavelength of a photon able to do this, in femtometres, is
Q15. Muons have a proper mean lifetime of 2.2 μs. A muon beam moves at 0.80c (c = 3.0×10⁸ m/s). The mean distance travelled before decaying, as measured in the laboratory, is
Q16. A metre stick moves along its length past an observer, who measures its length as 0.50 m. Its speed, as a fraction of c to two decimal places, is
Q17. A particle moves at 0.80c. The ratio of its kinetic energy to its rest energy is
Q18. An electron is confined within 1.0×10⁻¹⁰ m. Using Δx·Δp ≥ ħ/2 with ħ = 1.05×10⁻³⁴ J s, the minimum uncertainty in its momentum is
Q19. An X-ray tube operating at 20 kV has its voltage raised to 50 kV. Using hc = 1240 eV nm, the new minimum (cut-off) wavelength of the X-rays is
Q20. A pure silicon crystal is doped with a small amount of boron (group III). Which statement about the doped crystal is correct?
Q21. Which statement about a p–n junction diode under reverse bias is correct?
Q22. A full-wave rectifier is supplied from a 50 Hz AC mains source. The frequency of the ripple in the rectified output is
Q23. A transistor in the common-emitter configuration has current gain β = 100 and a base current of 40 μA. The emitter current is
Q24. An ideal operational amplifier is used as a non-inverting amplifier with R₁ = 2 kΩ to ground and a feedback resistor R_f = 18 kΩ. An input of 0.30 V gives an output of
Q25. A NOR gate has input A on one terminal and, on the other, the inverted input B (B passed through a NOT gate). For which input combination is its output 1?
Q26. ²³⁸U (Z = 92) undergoes one alpha decay followed by two beta-minus decays. The resulting nucleus is
Q27. Natural boron consists of 19.9% of boron-10 (10.0 u) and 80.1% of boron-11 (11.0 u). The average atomic mass is
Q28. A black body's temperature is changed so that its peak-emission wavelength falls from 1500 nm to 750 nm. By what factor does its total radiated power increase?
Q29. Hydrogen atoms are excited to the n = 5 level. The greatest number of different spectral lines that can be emitted as the atoms return to lower levels is
Q30. The ¹⁴C activity of an ancient wooden object is 25% of that of living wood. If the half-life of ¹⁴C is 5730 years, the object's age is