Question

Cesium frequently is used in photocells because its work function $(\mathbf{3}\mathbf{.}\mathbf{43}\mathbf{\times }{\mathbf{10}}^{-19}\mathbf{J})$ is the lowest of all the elements. Such photocells are efficient because the broadest range of wavelengths of light can eject electrons. What colors of light will eject electrons from cesium? What colors of light will eject electrons from selenium, which has a work function of $\mathbf{9}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{-19}\mathbf{J}$?

Short answer

Cesium emits green light and some parts of yellow light.

Selenium emits ultraviolet radiations.

Step-by-step solution

Given information

Work function of Cesium $\left({\mathrm{\varphi }}_{\mathrm{Cs}}\right)={\text{3.43×10}}^{\text{-19}}\text{J}$

Work function of Selenium$\left({\mathrm{\varphi }}_{\mathrm{Se}}\right)=9.5{\text{×10}}^{\text{-19}}\text{J}$

Work function

The minimum amount of energy required to excite electrons from a metal surface is known as the work function. Work function is a characteristic property of the metal.

$\mathrm{\varphi }={\mathrm{h\nu }}_0\left(1\right)$

Here,

$\begin{array}{l}\varphi =\text{work\hspace{0.17em}function}\\ h=\text{Plank's\hspace{0.17em}\hspace{0.17em}constant}\\ {\nu }_0=\text{frequency\hspace{0.17em}of\hspace{0.17em}incident\hspace{0.17em}light}\end{array}$

Minimum wavelength of light emitted by Cesium

Using equation (1), we can calculate the minimum wavelength of light required to excite electrons from the surface of Cesium.

Therefore, the minimum wavelength of light required is $5.79\times {10}^{-7}mor579nm$. This is within the visible range of the spectrum. The colors of light that are emitted.

Minimum wavelength of light emitted by Selenium

Similarly, we can calculate the minimum wavelength of the light required to excite electrons form Selenium surface.

Therefore, the minimum wavelength of light required is $2.09\times {10}^{-7}\mathrm{m}\mathrm{or}209\mathrm{nm}$. This falls under the ultraviolet region and hence no visible light would be emitted.