The intensity of characteristic X-rays depends on:
Answer: C
Characteristic X-ray intensity depends on the number of inner-shell electrons available (atomic number) and the number of incident electrons (beam current).
Q.663Hard
An electron transitions from n=3 to n=1 in a hydrogen atom. How many distinct spectral lines can be observed from all possible transitions?
Answer: C
Possible transitions: 3→1 (direct), 3→2, 2→1. Total = 3 distinct lines. The electron can go 3→2→1 or 3→1 directly.
Q.664Hard
In pair production, a photon with energy 3 MeV converts near a nucleus into an electron-positron pair. The rest mass energy of electron/positron is 0.51 MeV. The excess energy appears as:
Answer: A
In pair production: E_photon = 2m_e c² + KE_total. Excess = 3 - 2(0.51) = 1.98 MeV becomes kinetic energy of the pair.
Q.665Easy
The half-life of ¹⁴C is 5730 years. A sample contains 1 mg of ¹⁴C. After 11,460 years, the remaining mass will be:
Answer: A
11,460 years = 2 × 5730 years = 2 half-lives. After 2 half-lives: 1 × (21)² = 0.25 mg remains.
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Q.666Hard
For a nucleus, the neutron-to-proton ratio (N/Z) increases with mass number. This is because:
Answer: C
For heavy nuclei, the Coulomb repulsion between protons increases significantly. Extra neutrons (uncharged) help stabilize the nucleus without increasing repulsion, requiring N > Z for stability.
Q.667Medium
A photon of wavelength 100 pm strikes a stationary free electron. After Compton scattering at an angle of 60°, the wavelength of the scattered photon is found to be 102.4 pm. What is the kinetic energy of the recoil electron? (Given: h = 6.63 × 10⁻³⁴ J·s, c = 3 × 10⁸ m/s, mₑ = 9.1 × 10⁻³¹ kg)
Answer: A
Using Compton scattering formula: λ' - λ = (h/mₑc)(1 - cos θ). With given values, the wavelength shift is 2.4 pm. Using energy conservation, the incident photon energy is E₀ = hc/λ ≈ 12.4 keV. The scattered photon energy E' = hc/λ' ≈ 12.1 keV. The kinetic energy of electron = E₀ - E' ≈ 1.65 keV.
Q.668Easy
Which of the following is a direct bandgap semiconductor?
Answer: A
GaAs is a direct bandgap semiconductor where the minimum energy gap occurs at the same k-value, making it suitable for light emission. Si and Ge are indirect bandgap semiconductors.
Q.669Easy
At absolute zero temperature, the number of free electrons in an intrinsic semiconductor is:
Answer: B
At T = 0 K, all electrons remain in the valence band. No thermal energy is available to excite electrons to the conduction band, so free electrons are zero.
Q.670Easy
The bandgap of silicon at room temperature (300 K) is approximately:
Answer: B
Silicon has a bandgap of approximately 1.1 eV at 300 K. This is a standard value used in semiconductor physics and device design.
Q.671Medium
In an n-type semiconductor, the Fermi level lies:
Answer: B
In n-type semiconductors, donor levels introduce electrons near the conduction band, shifting the Fermi level upward, making it closer to the conduction band than to the valence band.
Q.672Medium
The conductivity of a semiconductor increases with temperature because:
Answer: D
While mobility decreases with temperature due to increased phonon scattering, the exponential increase in intrinsic carrier concentration dominates, resulting in net increase in conductivity. However, (b) is the primary reason.
Q.673Easy
A p-type semiconductor is created by doping silicon with:
Answer: C
Boron is a Group III element (trivalent) that acts as an acceptor in silicon, creating holes and forming p-type semiconductor. Phosphorus, Arsenic, and Antimony are Group V elements (pentavalent) forming n-type semiconductors.
Q.674Medium
The intrinsic carrier concentration ni in a semiconductor is given by: ni = √(NcNv)exp(-Eg/2kT). What does Nc represent?
Answer: B
Nc is the effective density of states in the conduction band, which depends on the effective mass of electrons and temperature. Similarly, Nv is for the valence band.
Q.675Medium
In forward biasing of a p-n junction, the depletion region width:
Answer: B
Forward bias reduces the potential barrier at the junction, allowing carriers to move across more easily. This reduces the depletion region width, which is inversely related to the applied voltage.
Q.676Medium
The reverse saturation current in a p-n junction diode depends on:
Answer: B
Reverse saturation current I0 is determined by intrinsic carrier concentration (ni), diffusion coefficient (D), and junction properties. It is independent of reverse voltage but depends strongly on temperature.
Q.677Medium
Zener breakdown in a semiconductor occurs when:
Answer: B
Zener breakdown involves quantum mechanical tunneling of electrons directly from valence band to conduction band under strong reverse electric field. It occurs in heavily doped junctions at lower voltages than avalanche breakdown.
Q.678Medium
At thermal equilibrium in a semiconductor, the product of electron and hole concentrations is:
Answer: B
The mass action law states ne·nh = ni² at thermal equilibrium, regardless of doping type. This is a fundamental relationship derived from Fermi-Dirac statistics.
Q.679Medium
A BJT transistor operates in saturation region when:
Answer: B
In saturation, both junctions are forward biased, allowing maximum current flow. In active region, BE is forward and CB is reverse biased. In cutoff, both are reverse biased.
Q.680Medium
The Hall effect coefficient (RH) for an n-type semiconductor is:
Answer: B
For n-type semiconductors, charge carriers are electrons (negative), so the Hall coefficient is negative. For p-type (holes), it is positive. The sign determines carrier type.
