Question

The work function of an element is the energy required to remove an electron from the surface of the solid. The work function for rhodium is 480.5 kJ/mol (that is, it takes 480.5 kJ of energy to remove 1 mole of electrons from 1 mole of Rh atoms on the surface of Rh metal). What is the maximum wavelength of light that can remove an electron from an atom in rhodium metal?

Answer 1

Answer:

$\lambda=249.2\ nm$

Explanation:

Given that:

The work function of the rhodium = 480.5 kJ/mol

It means that

1 mole of electrons can be removed by applying of 480.5 kJ of energy.

Also,

1 mole = $6.023\times 10^{23}\ electrons$

So,

$6.023\times 10^{23}$ electrons can be removed by applying of 480.5 kJ of energy.

1 electron can be removed by applying of $\frac {480.5}{6.023\times 10^{23}}\ kJ$ of energy.

Energy required = $79.78\times 10^{-23}\ kJ$

Also,

1 kJ = 1000 J

So,

Energy required = $79.78\times 10^{-20}\ J$

Also, $E=\frac {h\times c}{\lambda}$

Where,  

h is Plank's constant having value $6.626\times 10^{-34}\ Js$

c is the speed of light having value $3\times 10^8\ m/s$

So,

$79.78\times 10^{-20}=\frac {6.626\times 10^{-34}\times 3\times 10^8}{\lambda}$

$\lambda=\frac{6.626\times 10^{-34}\times 3\times 10^8}{79.78\times 10^{-20}}$

$\lambda=\frac{10^{-26}\times \:19.878}{10^{-20}\times \:79.78}$

$\lambda=\frac{19.878}{10^6\times \:79.78}$

$\lambda=2.4916\times 10^{-7}\ m$

Also,

1 m = 10⁻⁹ nm

So,

$\lambda=249.2\ nm$