Neco 2017 Physics Question 30

Practice objective / multiple choice question 30 from the 2017 Neco Physics examination.

Neco 2017 Physics Objective / Multiple Choice Hard Difficulty
Question 30 NECO • 2017 • PHYSICS • objective

A hydrogen atom is excited to the \(n=4\) energy level. It can return to the ground state (\(n=1\)) by either (i) a direct transition \(4\rightarrow1\) emitting a photon of wavelength \(\lambda_{1}\), or (ii) a two‑step transition \(4\rightarrow2\) followed by \(2\rightarrow1\) emitting photons of wavelengths \(\lambda_{2}\) and \(\lambda_{3}\) respectively. (a) Calculate \(\lambda_{1},\lambda_{2},\lambda_{3}\) using the Rydberg formula (\(R_{H}=1.097373\times10^{7}\ \text{m}^{-1}\)). (b) Determine the ratio \(\dfrac{E_{2}+E_{3}}{E_{1}}\) where \(E_{i}=hc/\lambda_{i}\). (c) If the atom is placed in a uniform magnetic field of \(B=2.0\ \text{T}\), calculate the Zeeman energy splitting for the transition between the \(n=2,\ l=1,\ m_{l}=+1\) and \(m_{l}=0\) sub‑levels (ignore spin). Use the Bohr magneton \(\mu_{B}=9.274\times10^{-24}\ \text{J·T}^{-1}\).

Answer Options

A. λ₁≈102 nm, λ₂≈434 nm, λ₃≈109 nm; (E₂+E₃)\/E₁≈0.95; Zeeman splitting ΔE≈2.10×10⁻²³ J
B. λ₁≈98.5 nm, λ₂≈480 nm, λ₃≈122 nm; (E₂+E₃)\/E₁≈0.99; Zeeman splitting ΔE≈1.90×10⁻²³ J
C. λ₁≈95.0 nm, λ₂≈500 nm, λ₃≈124 nm; (E₂+E₃)\/E₁≈1.05; Zeeman splitting ΔE≈1.70×10⁻²³ J
Correct Answer D. λ₁≈97.2 nm, λ₂≈486 nm, λ₃≈121.5 nm; (E₂+E₃)/E₁≈1.00; Zeeman splitting ΔE≈1.85×10⁻²³ J
Correct Answer
D
Correct Option:
λ₁≈97.2 nm, λ₂≈486 nm, λ₃≈121.5 nm; (E₂+E₃)/E₁≈1.00; Zeeman splitting ΔE≈1.85×10⁻²³ J

About This Question

This is Neco 2017 Physics Question 30. It is one of the objective questions from the 2017 Neco Physics examination.

Difficulty level: Hard .

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