One fairly crude method of determining the size of a molecule is to treat the molecule as an infinite square well (a box) with an electron trapped inside, and to measure the wavelengths of emitted photons. If the photon emitted during the n = 2 to n = 1 transition has wavelength 1940 nm, what is the width of the molecule? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34J ∙ s, m_el = 9.11 × 10^-31 kg) A) 1.33 nm B) 1.12 nm C) 1.21 nm D) 1.45 nm

Question

Quizplus · Accepted Answer

The energy of a photon is given by E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength. The energy difference between the n = 2 and n = 1 states is given by ΔE = E₂ - E₁ = (3/2)hc/λ. The width of the molecule is given by L = √(2mΔE/h²), where m is the mass of the electron. Substituting the given values, we get L = 1.33 nm.

One Fairly Crude Method of Determining the Size of a Molecule