Question

Photovoltaic cells convert solar energy into electricity. Calculate the wavelength of light (in nm) required for mercury (Φ =7.22 × 10–19 J) to emit an electron. Then determine whether or not mercury could be used to generate electricity from the sun. Assume that most of the electromagnetic energy from the sun is in the visible region near 500 nm.

Answer 1

Answer:

275.3 nm is the wavelength of light required for mercury.

Mercury can not be used to generate electricity from the sun because wavelength at which mercury will emit an electron is smaller than 500 nm.

Explanation:

The wavelength of light required for mercury  to emit an electron.

The wavelength of the radiation = $\lambda$

Energy required fro mercury to to emit an electron = E

Energy required fro mercury to to emit an electron will the energy if the radiation = E' = $7.22\times 10^{-19} J$

E' = E

To calculate the wavelength of light, we use the equation:

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

where,

$\lambda$ = wavelength of the light  

h = Planck's constant = $6.626\times 10^{-34} Js$

c = speed of light = $3\times 10^8m/s$

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

$=\frac{6.626\times 10^{-34} Js\times 3\times 10^8m/s}{7.22\times 10^{-19} J}$

$\lambda =2.753\times 10^{-7} m=2.753\times 10^{-7}\times 10^ nm =275.3 nm$

Wavelength of the sun light in the visible region = 500 nm

500 nm > 275.3 nm

$E\propto \frac{1}{\lambda }$

Less energy < more energy

So, this means that mercury can not be used to generate electricity from the sun.