A monochromatic light beam is incident on the surface of a metal having a work function of $2.50$ $\mathrm { eV }$. If a $1.0 - \mathrm { V }$ stopping potential is required to make the electron current zero, what is the wavelength of light? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} \right)$
A) $423 \mathrm {~nm}$
B) $744 \mathrm {~nm}$
C) $355 \mathrm {~nm}$
D) $497 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The energy of the incident photons is equal to the work function plus the stopping potential energy. Using the photoelectric equation $E = \phi + eV_s$, where $\phi = 2.50 \, \mathrm{eV}$ and $eV_s = 1.0 \, \mathrm{eV}$, the total energy is $3.50 \, \mathrm{eV}$. Converting this to joules gives $3.50 \times 1.60 \times 10^{-19} \, \mathrm{J}$. Using $E = \frac{hc}{\lambda}$, solve for $\lambda$ to find the wavelength: $\lambda = \frac{hc}{E}$. Substituting the values gives $\lambda \approx 355 \, \mathrm{nm}$.

A Monochromatic Light Beam Is Incident on the Surface of a Metal