Question

An orbiting satellite can charge by the photoelectric effect when sunlight ejects electrons from its outer surface. Satellites must be designed to minimize such charging because it can ruin the sensitive microelectronics. Suppose a satellite is coated with platinum, a metal with a very large function $\left(\varphi =5.32eV\right)$. Find the longest wavelength of incident sunlight that can eject an electron from the platinum.

Short answer

The value of longest wavelength of incident sunlight is 233 nm.

Step-by-step solution

Identification of the given data

The given data is listed below as-

The work function is $\varphi =5.32\mathrm{eV}$

Significance of the photoelectric equation.

The photoelectric equation which is used to find the wavelength is given by-

$\frac{hc}{\lambda }=\varphi +K_m$

Here, the work function depends on the material and condition of the surface and not on the wavelength of incident light.

To determine a value of the longest wavelength of incident sunlight

The value of maximum kinetic energy of a photon is assumed as zero to find the longest wavelength of incident sunlight i.e., $K_{\max }=0$

Therefore, the photoelectric equation is given by-

$\frac{hc}{\lambda }=\varphi +K_{\max }$

Now, $K_{\max }=0$

Therefore, $\frac{hc}{{\lambda }_{\max }}=\varphi$

Substitute for, hc = 1240 eV.nm, $\varphi =5.32\mathrm{nm}$in the above equation.

$\begin{array}{c}{\lambda }_{\max }=\frac{hc}{\varphi }\\ =\frac{1240\mathrm{eV}.\mathrm{nm}}{5.32\mathrm{nm}}\\ =233\mathrm{nm}\end{array}$

Thus, the value of the longest wavelength of incident sunlight is 233 nm.