UPSC Combined Geo-Scientist, Mains · 2023 · Mains Paper II
Q11(a). Box length from the longest-wavelength transition
Question
An electron confined in a one-dimensional box undergoes the longest wavelength transition at 400 nm. What is the length of the box in nm?
Answer in brief
The longest wavelength is the n = 1 → 2 transition: L = √(3hλ/8mₑc) = 6.03 × 10⁻¹⁰ m = 0.603 nm.
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Coversparticle in a 1-D boxbox lengthenergy levelslongest wavelength transitionquantum chemistry numerical
All parts of Question 11
- 11(a) Box length from the longest-wavelength transition10 marks
- 11(b) Cell edge of silicon from its density10 marks