AQA AS Level Physics Paper 2, June 2023: Question 12

De-excitation and Photon Frequencies

Difficulty: Medium

What this question tests

This question assesses your understanding of atomic energy levels, electron de-excitation pathways, and the relationship between energy transitions and emitted photon frequencies (using ΔE = hf ). You must systematically account for all possible single-step and multi-step transitions from a higher energy level down to the ground state.

Question 1.2

De-excitation of atoms from n = 4 to n = 1

✅ Correct Answer

Option D (6) is the correct answer.

💡 Key Knowledge

Each unique energy change ( ΔE ) during a transition produces a photon of a specific frequency according to f = ΔE / h .
De-excitation can happen directly to the ground state or via intermediate energy levels.
The total number of possible transitions between n levels can be calculated using the mathematical combination formula: N = n(n - 1) / 2 .

🧠 Exam Technique

Do not just guess or count transitions visually on the diagram. List all possible start and end level pairs logically in order of upper levels down to lower levels to avoid missing any combinations or double-counting.

❌ Common Errors

A common mistake is assuming atoms only drop straight down to the ground state ( n = 1 ) in one go, or only counting downward steps of 1 level (which would incorrectly yield 3 transitions).

📐 Step-by-Step Breakdown

Let's map out every possible downward transition from n = 4 :

From n = 4: Can drop to n = 3 , n = 2 , or n = 1 (3 transitions)
From n = 3: Can drop to n = 2 , or n = 1 (2 transitions)
From n = 2: Can drop to n = 1 (1 transition)

Summing them up: 3 + 2 + 1 = 6 distinct photon frequencies.

Alternatively, using the formula for n = 4 : 4 × (4 - 1) / 2 = 4 × 3 / 2 = 6 .

Mark Scheme Allocation: 1 mark total for selecting option D.