An electron is confined in a harmonic oscillator potential w

An electron is confined in a harmonic oscillator potential well. What is the longest wavelength of light that the electron can absorb if the net force on the electron behaves as though it has a spring constant of 74 N/m? (m_el = 9.11 times 10^-31 kg, c = 3.00 times 10^8 m/s, 1 eV = 1.60 times 10^-19 J. h = 1.055 times 10^-34 J middot s, h = 6.626 times 10^-34 J middot s) 230 nm 220 nm 210 nm 200 nm

Solution

E_n = (n +1/2) h_bar w

w = sqrt (k / m)

h c / lambda_max = h_bar sqrt(k/m)

lambda_max = 2 pi c sqrt(m/k)

= 2 * pi * 3 * 10⁸ * sqrt(9.11*10^-31 / 74 )

= 210 nm