Question

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 × 10-31 kg, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J, ℏ = 1.055 × 10-34 J · s, h = 6.626 × 10-34 J · s)

Answer 1

Answer:

The longest wavelength of light is 209 nm.

Explanation:

Given that,

Spring constant = 74 N/m

Mass of electron $m= 9.11\times10^{-31}\ kg$

Speed of light $c= 3\times10^{8}\ m/s$

We need to calculate the frequency

Using formula of frequency

$f =\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}$

Where, k= spring constant

m = mass of the particle

Put the value into the formula

$f=\dfrac{1}{2\pi}\sqrt{\dfrac{74}{9.11\times10^{-31}}}$

$f=1.434\times10^{15}\ Hz$

We need to calculate the longest wavelength that the electron  can absorb

$\lambda=\dfrac{c}{f}$

Where, c = speed of light

f = frequency

Put the value into the formula

$\lambda =\dfrac{3\times10^{8}}{1.434\times10^{15}}$

$\lambda=2.092\times10^{-7}\ m$

$\lambda=209\ nm$

Hence, The longest wavelength of light is 209 nm.