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, , A) 1.33 nm B) 1.12 nm C) 1.21 nm D) 1.45 nm

Question

Quizplus · Accepted Answer

The energy of a particle in an infinite square well is given by E_n=(n^2*h^2)/(8mL^2), where h is Planck's constant, m is the mass of the particle, and L is the width of the well. The wavelength of a photon emitted during the transition from n=2 to n=1 is given by λ = c/f = hc/(E_2 - E_1), where f is its frequency, c is the speed of light, and h is Planck's constant.
 
Combining these equations and solving for L, we get L = sqrt[(n^2*h^2)/(8m*(E_2 - E_1))]
 
Plugging in the given values and solving, we get L = 1.33 nm. Therefore, the molecule's width is 1.33 nm.

One Fairly Crude Method of Determining the Size of a Molecule