Question

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

Answer 1

Answer:

$\lambda=428.04\ nm$

Explanation:

The work function of the lithium = 279.7 KJ/mol  (Source)

It means that  

1 mole of electrons can be removed by applying of 279.7 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 279.7 kJ of energy.

1 electron can be removed by applying of $\frac {279.7}{6.023\times 10^{23}}\ kJ$ of energy.

Energy required = $46.44\times 10^{-23}\ kJ$

Also,  

1 kJ = 1000 J

So,  

Energy required = $46.44\times 10^{-20}\ J$

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,  

$46.44\times 10^{-20}=\frac {6.626\times 10^{-34}\times 3\times 10^8}{\lambda}$

$\lambda=\frac{6.626\times 10^{-34}\times 3\times 10^8}{46.44\times 10^{-20}}$

$\lambda=\frac{10^{-26}\times \:19.878}{10^{-20}\times \:46.44}$

$\lambda=\frac{19.878}{10^6\times \:46.44}$

$\lambda=4.2804\times 10^{-7}\ m$

Also,  

1 m = 10⁻⁹ nm

So,  

$\lambda=428.04\ nm$