Question

It takes 258 kJ/mol to eject electrons from a certain metal surface. What is the longest wavelength of light (nm) that can be used to eject electrons from the surface of this metal via the photoelectric effect?

Answer 1

Answer: The wavelength of light that can be used is 464 nm

Explanation:

We are given:

Energy of the electrons = 258 kJ/mol

This is the energy of the 1 mole of electrons

To calculate the energy of 1 electron, we divide the energy by Avogadro's number:

$\text{Energy of 1 electron}=\frac{E}{N_A}$

$N_A=6.022\times 10^{23}$

$E=258kJ/mol=2.58\times 10^5J/mol$     (Conversion factor:  1 kJ = 1000 J)

Putting values in above equation, we get:

$\text{Energy of 1 electron}=\frac{2.58\times 10^5}{6.022\times 10^{23}}=4.28\times 10^{-19}J$

To calculate the energy of one photon, we use Planck's equation, which is:

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

where,

h = Planck's constant = $6.625\times 10^{-34}J.s$

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

Energy of 1 electron = $4.28\times 10^{-19}J$

Putting values in above equation, we get:

$4.28\times 10^{-19}J=\frac{6.625\times 10^{-34}J.s\times 3\times 10^8m/s}{\lambda}\\\\\lambda=\frac{6.625\times 10^{-34}\times 3\times 10^8m/s}{4.28\times 10^{-19}}=4.64\times 10^{-7}m$

Converting this to nano meters, we use the conversion factor:

$1m=10^9nm$

So, $4.64\times 10^{-7}m\times \frac{10^9nm}{1m}=464nm$

Hence, the wavelength of light that can be used is 464 nm