What wavelength of light does an electron confined in a rigid box of 1-nm length absorb? Assume the electron starts in the ground state.
A)1.1 µm
B)0.5 µm
C)120 nm
D)8.9 µm

Question

Quizplus · Accepted Answer

The energy difference between the ground state and the first excited state is given by:$$\Delta E = E_2 - E_1 = \frac{h^2}{8mL^2}$$where h is Planck's constant, m is the mass of the electron, and L is the length of the box.The wavelength of light absorbed is given by:$$\lambda = \frac{hc}{\Delta E}$$Substituting the values given in the question, we get:$$\lambda = \frac{(6.626 	imes 10^{-34} 	ext{ J s})(3 	imes 10^8 	ext{ m/s})}{8(9.109 	imes 10^{-31} 	ext{ kg})(1 	imes 10^{-9} 	ext{ m})^2}$$$$\lambda = 1.1 \mu 	ext{m}$$

What Wavelength of Light Does an Electron Confined in a Rigid