Question

The work function of a metal is 3.45 eV. Calculate the maximum wavelength of a photon that can eject photoelectrons from the metal

Answer 1

We are asked to determine the maximum wavelength of a photon that can eject photoelectrons from a metal given its work function. To do that we will use the following formula:

$\lambda=\frac{hc}{E}$

Where:

$\begin{gathered} \lambda=\text{ wavelength} \\ h=\text{ plank's constant} \\ c=\text{ speed of light} \\ E=\text{ work function} \end{gathered}$

First, we will convert the work function from eV to Joules. To do that we will use the following conversion factor:

$1eV=1.6\times10^{-19}J$

Multiplying by the conversion factor we get:

$3.45eV\times\frac{1.6\times10^{-19}J}{1eV}=5.53\times10^{-19}J$

Plank's constant is equivalent to:

$h=6.63\times10^{-34}Js$

The speed of light is equivalent to:

$c=3\times10^8\frac{m}{s}$

Now, we plug in the values in the formula:

$\lambda=\frac{(6.63\times10^{-34}Js)(3\times10^8\frac{m}{s})}{5.53\times10^{-19}J}$

Solving the operations:

$\lambda=3.6\times10^{-7}m$

And thus we have determined the wavelength.