Question 1

An alpha particle (He-4 nucleus) has a mass defect of 0.0305 u. What is its binding energy? (1 u = 931 MeV/c²)

Accepted Answer

Binding Energy = mass defect × c² = 0.0305 × 931 ≈ 28.4 MeV.

Question 2

In a semiconductor material, the forbidden energy gap (band gap) is defined as:

Accepted Answer

The band gap Eg is the minimum energy difference between the valence band and conduction band, which must be overcome to create a free electron-hole pair.

Question 3

The ionization energy of a hydrogen atom is the energy required to remove the electron from the first orbit. This value is:

Accepted Answer

Ionization energy equals the magnitude of ground state energy: |E₁| = 13.6 eV.

Question 4

The radius of a nucleus is given by R = R₀A^(1/3), where R₀ ≈ 1.2 fm. If nucleus A has mass number 8 and nucleus B has mass number 27, what is the ratio of their radii R_A : R_B?

Accepted Answer

R_A/R_B = (8/27)^(1/3) = 2/3, so R_A : R_B = 2 : 3.

Question 5

A semiconductor has an intrinsic carrier concentration of ni = 1.5 × 10¹⁰ cm⁻³ at 300 K. If the semiconductor is doped with donor impurities to make it n-type with carrier concentration n = 1.5 × 10¹⁵ cm⁻³, what is the hole concentration p in this n-type semiconductor?

Accepted Answer

In thermal equilibrium, the mass action law states n·p = ni², therefore p = ni²/n = (1.5 × 10¹⁰)²/(1.5 × 10¹⁵) = 1.5 × 10⁵ cm⁻³.

Question 6

A p-n junction diode is forward biased with an applied voltage of 0.6 V. If the thermal voltage kT/e at room temperature is 0.026 V, what is the approximate diode current relative to its reverse saturation current I₀ using the ideal diode equation I = I₀(e^(eV/kT) − 1)?

Accepted Answer

With V = 0.6 V and kT/e = 0.026 V, eV/kT ≈ 23.08, so e^(23.08) ≈ 11 × 10⁹, which gives I ≈ 11 × 10⁹ × I₀ or approximately 23000 × I₀ (order of magnitude).

Question 7

The energy of an electron in the second orbit (n=2) of a hydrogen atom is -3.4 eV. What is the energy of the electron in the first orbit (n=1)?

Accepted Answer

Energy in Bohr model: Eₙ = -13.6/n² eV, so E₁ = -13.6/1² = -13.6 eV.

Question 8

Which of the following statements about the ground state of a hydrogen atom is correct?

Accepted Answer

In the ground state of hydrogen, the electron is in the n=1 orbit, which is the lowest possible energy state according to Bohr's model.

Question 9

The binding energy per nucleon is maximum for nuclei with mass number around:

Accepted Answer

Iron-56 has the highest binding energy per nucleon (~8.8 MeV), making it the most stable nucleus.

Question 10

A nucleus undergoes beta-minus decay. What happens to the atomic number (Z) and mass number (A)?

Accepted Answer

In β⁻ decay, a neutron converts to a proton, emitting an electron; Z increases by 1 while A stays constant.

Question 11

An electron accelerated through a potential difference of 50 V has a de Broglie wavelength of 1.73 × 10⁻¹⁰ m. Which statement correctly describes the dual nature illustrated here?

Accepted Answer

The electron's acceleration (particle behavior) and associated de Broglie wavelength (wave behavior) together demonstrate dual nature of matter.

Question 12

In nuclear fission, a heavy nucleus splits into two lighter nuclei. Which statement is correct?

Accepted Answer

Fission converts mass defect into kinetic energy of products (E=mc²); lighter nuclei have higher binding energy per nucleon.

Question 13

The de Broglie wavelength of a moving particle is given by λ = h/p. If an electron (mass = 9.1 × 10⁻³¹ kg) moves with velocity 2 × 10⁶ m/s, calculate its de Broglie wavelength. (h = 6.63 × 10⁻³⁴ J·s)

Accepted Answer

λ = h/(mv) = 6.63 × 10⁻³⁴ / (9.1 × 10⁻³¹ × 2 × 10⁶) = 3.64 × 10⁻¹⁰ m, showing matter exhibits wave properties.

Question 14

Which of the following statements correctly describes the energy band structure of a semiconductor at 0 K?

Accepted Answer

At absolute zero temperature, all electrons occupy the lowest available energy states; the valence band is completely filled and the conduction band is empty in an intrinsic semiconductor.

Question 15

In the photoelectric effect, Einstein's photon theory explains that light consists of discrete energy packets. Which phenomenon directly proves the particle nature of radiation?

Accepted Answer

The photoelectric effect and threshold frequency cannot be explained by wave theory alone; they require light to behave as particles (photons) with discrete energies.

Question 16

According to Bohr's model of the hydrogen atom, the radius of the first orbit (Bohr radius) is approximately:

Accepted Answer

The Bohr radius a₀ = 0.53 Å is the characteristic radius of the first electron orbit in a hydrogen atom.

Question 17

A light wave of wavelength 500 nm is diffracted through a slit, and simultaneously, individual photons from this light eject electrons from a photoelectric surface. Which aspect of dual nature is demonstrated respectively?

Accepted Answer

Diffraction is a wave phenomenon (light bends around obstacles), while photoelectric effect demonstrates particle nature (photons transfer discrete energy to electrons).

Question 18

An electron transitions from the third orbit (n=3) to the second orbit (n=2) in a hydrogen atom. The energy of the emitted photon is:

Accepted Answer

ΔE = 13.6(1/2² - 1/3²) = 13.6(1/4 - 1/9) = 13.6 × 5/36 ≈ 1.9 eV.

Question 19

A photon of frequency 6 × 10¹⁵ Hz is incident on a metal surface. If the Planck's constant h = 6.63 × 10⁻³⁴ J·s, calculate the energy of the photon.

Accepted Answer

Energy of photon E = hf = 6.63 × 10⁻³⁴ × 6 × 10¹⁵ = 3.98 × 10⁻¹⁸ J, demonstrating photon's particle nature.

Question 20

A silicon semiconductor is doped with acceptor impurities to create a p-type semiconductor. Which of the following is the primary charge carrier in this p-type material?

Accepted Answer

In a p-type semiconductor, acceptor atoms create holes in the valence band, and these holes become the majority carriers responsible for electrical conduction.

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