An electron moves from an energy level of -8.6 eV to another level of -3.5 eV. Determine the frequency of the…

Analyze the question: An electron absorbs radiation and moves up from -8.6 eV to -3.5 eV. We need the frequency of that radiation.

Concept: The energy absorbed equals the difference between the two levels, and E = hf, so f = ΔE / h.

(The question prints the constants as 1.6 × 10^19 and 6.6 × 10^34. The signs are missing. They should be 1.6 × 10⁻¹⁹ J and 6.6 × 10⁻³⁴ Js.)

Solution:

1. Energy difference: ΔE = -3.5 - (-8.6) = 5.1 eV

2. Convert to joules: ΔE = 5.1 × 1.6 × 10⁻¹⁹ = 8.16 × 10⁻¹⁹ J

3. Find the frequency: f = ΔE / h = (8.16 × 10⁻¹⁹) / (6.6 × 10⁻³⁴) f ≈ 1.236 × 10¹⁵ Hz ≈ 1.24 × 10¹⁵ Hz

Tip: In energy-level questions, always subtract the lower level from the higher one (final − initial for absorption) to get a positive energy. Also convert eV to joules before dividing by h. A quick check is that 5.1 eV is roughly 1.2 × 10¹⁵ Hz, since 1 eV corresponds to about 2.4 × 10¹⁴ Hz.