Board-style MCQs and past-paper numericals in the BIEK / Sindh Board pattern. Tap an option to check yourself instantly. Solved questions are at the bottom.
Multiple-choice questions
Solved numericals (past papers)
Energy of the n = 2 level in hydrogen
For hydrogen, Eₙ = −13.6/n² eV. Find the energy of the first excited state (n = 2).
E₂ = −13.6/2² = −13.6/4 = −3.4 eV
Energy and wavelength of a photon (Hα line)
An electron falls from n = 3 to n = 2 in hydrogen. Find the photon energy and wavelength.
E₃ = −13.6/9 = −1.51 eV, E₂ = −3.40 eV
ΔE = E₃ − E₂ = −1.51 − (−3.40) = 1.89 eV
λ = hc/E = 1240 eV·nm / 1.89 eV = 656 nm (red Hα line)
Wavelength from the Rydberg formula (first Lyman line)
Use 1/λ = R(1/n₁² − 1/n₂²) with R = 1.097 × 10⁷ m⁻¹ for the n = 2 → 1 transition.
1/λ = 1.097×10⁷ (1/1² − 1/2²) = 1.097×10⁷ × (1 − 0.25) = 1.097×10⁷ × 0.75 = 8.23×10⁶ m⁻¹
λ = 1/8.23×10⁶ = 1.215 × 10⁻⁷ m (121.5 nm, ultraviolet)
Ionisation energy of hydrogen
Find the energy needed to remove the electron from the ground state (n = 1 → ∞).
E∞ − E₁ = 0 − (−13.6) = 13.6 eV
In joules: 13.6 × 1.6×10⁻¹⁹ = 2.18 × 10⁻¹⁸ J
Radius of the n = 2 Bohr orbit
The Bohr radius is r₁ = 0.529 Å and rₙ = n²r₁. Find r₂.
r₂ = 2² × 0.529 = 4 × 0.529 = 2.12 Å (2.12 × 10⁻¹⁰ m)
Minimum X-ray wavelength from an X-ray tube
An X-ray tube is operated at 50 kV. Find the shortest (cut-off) wavelength produced.
eV = hc/λ_min ⇒ λ_min = hc/(eV) = 1240 eV·nm / 50000 eV = 0.0248 nm (2.48 × 10⁻¹¹ m)