# The threshold frequency of silver is 9.71×1015 Hz. What is the work function of silver?

## Planck’s constant is 6.63 × 10−34 J · s. Answer in units of eV.

May 16, 2018

$W = 40.2$ $\text{eV}$

#### Explanation:

Threshold frequency is related to the work function by the following equation:

${f}_{0} = \frac{W}{h}$; where ${f}_{0}$ is the threshold frequency, $W$ is the work function, and $h$ is the Planck constant.

We can rearrange this equation to solve for $W$:

$R i g h t a r r o w W = {f}_{0} h$

Let's plug in the given values:

$R i g h t a r r o w W = \left(9.71 \times {10}^{15} \times 6.63 \times {10}^{- 34}\right)$ $\text{J}$

$R i g h t a r r o w W = 6.43773 \times {10}^{- 18}$ $\text{J}$

However, we need to answer in units of $\text{eV}$:

$R i g h t a r r o w W = \left(\frac{6.43773 \times {10}^{- 18}}{1.6 \times {10}^{- 19}}\right)$ $\text{eV}$

$\therefore W \approx 40.2$ $\text{eV}$