ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Electronics, Modern, Atomic and Nuclear Physics (Set 7): 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. Taking h = 4.14 × 10⁻¹⁵ eV s, the energy of a photon of frequency 6 × 10¹⁴ Hz is:
Answer: C. 2.48 eV
Explanation: E = hf = (4.14 × 10⁻¹⁵)(6 × 10¹⁴) = 2.48 eV.
Q2. Light of photon energy 4.5 eV falls on a metal of work function 2.5 eV. The stopping potential is:
Answer: B. 2.0 V
Explanation: K_max = hf − φ = 2.0 eV, so V₀ = 2.0 V.
Q3. Taking hc = 1240 eV nm, the threshold wavelength for a metal of work function 2.48 eV is:
Answer: D. 500 nm
Explanation: λ₀ = hc/φ = 1240/2.48 = 500 nm.
Q4. Taking h = 6.63 × 10⁻³⁴ J s, the momentum of a photon of wavelength 500 nm is:
Answer: A. 1.33 × 10⁻²⁷ kg m/s
Explanation: p = h/λ = 6.63 × 10⁻³⁴/(5 × 10⁻⁷) = 1.33 × 10⁻²⁷ kg m/s.
Q5. Taking h = 6.63 × 10⁻³⁴ J s, a 0.1 kg ball moving at 6.63 m/s has a de Broglie wavelength of:
Answer: A. 10⁻³³ m
Explanation: λ = h/mv = 6.63 × 10⁻³⁴/(0.1 × 6.63) = 10⁻³³ m, far too small to observe.
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Q6. In Compton scattering, the shift in wavelength is Δλ = (h/mc)(1 − cosθ), with h/mc = 2.43 pm. For a photon scattered backwards (θ = 180°), the shift is:
Q7. With R = 1.097 × 10⁷ m⁻¹, the shortest wavelength (series limit) of the Balmer series is:
Q8. Taking the Bohr radius a₀ = 0.053 nm, the radius of the n = 3 orbit of hydrogen is:
Q9. The activity of a radioactive source falls from 800 Bq to 100 Bq in 30 minutes. Its half-life is:
Q10. A nuclide has a half-life of 20 s. Taking ln 2 = 0.693, its mean life 1/λ is:
Q11. Taking proton mass 1.0073 u, neutron mass 1.0087 u, ⁴He nuclear mass 4.0015 u and 1 u = 931.5 MeV, the binding energy per nucleon of ⁴He is:
Q12. A ²³⁸₉₂U nucleus emits one alpha particle and then two beta (β⁻) particles. The resulting nucleus has mass number A and atomic number Z equal to:
Q13. A reactor releases 200 MeV per fission and delivers a thermal power of 640 MW. Taking 1 MeV = 1.6 × 10⁻¹³ J, the number of fissions per second is:
Q14. Taking c = 3 × 10⁸ m/s, the energy equivalent of a mass of 1 mg is:
Q15. A spaceship moves at 0.6c relative to Earth. A clock on the ship measures a proper interval of 8 s. The Earth observers measure this interval as:
Q16. Taking Wien's constant as 2.9 × 10⁻³ m K, a star whose radiation peaks at 500 nm has a surface temperature of about:
Q17. A black body's absolute temperature is raised from 300 K to 900 K. According to Stefan's law, the power it radiates increases by a factor of:
Q18. Using Δx Δp ≥ ħ/2 with ħ = 1.05 × 10⁻³⁴ J s, the minimum uncertainty in the momentum of an electron localised to Δx = 0.5 × 10⁻¹⁰ m is:
Q19. Taking hc = 1240 eV nm, the minimum wavelength in the X-rays from a tube operated at 50 kV is:
Q20. For laser action, population inversion is the condition in which:
Q21. A 3.02 MeV photon produces an electron–positron pair (rest energy 0.51 MeV each). The total kinetic energy shared by the pair is:
Q22. When germanium is doped with a small amount of gallium (a trivalent impurity), the crystal becomes:
Q23. A silicon p–n junction diode is reverse biased with a moderate voltage. The small current that still flows is due to:
Q24. A full-wave rectifier is supplied from a 50 Hz AC mains. The fundamental frequency of the ripple in its output is:
Q25. A transistor in common-emitter mode has current gain β = 100. With a base current of 30 μA, the emitter current is:
Q26. A NOR gate has its two inputs joined together to form a single input. The gate then behaves as:
Q27. A non-inverting op-amp amplifier has Rf = 90 kΩ and R₁ = 10 kΩ, with gain 1 + Rf/R₁. For an input of 0.15 V the output voltage is:
Q28. A hydrogen atom in its ground state absorbs a photon of energy 12.09 eV (energy levels −13.6/n² eV). It is excited to the level:
Q29. Monochromatic light above the threshold frequency falls on a photocell. The light's intensity is doubled while its frequency is unchanged. The saturation current and the maximum kinetic energy of the photoelectrons become, respectively:
Q30. A laser emits 2 mW at a wavelength of 663 nm. Taking h = 6.63 × 10⁻³⁴ J s and c = 3 × 10⁸ m/s, the number of photons emitted per second is about: