When electromagnetic radiations of wave length 300nm falls on the surface of sodium, electrons are emitted with a kinetic energy of `1.68xx10^(5) J "mol"^(-1)` . What is the minimum energy needed to remove an electron from sodium ? What is the maximum wavelength that will cause a photoelectron to be emitted ?

Explanation

The energy (E) of a 300 nm photon is given by
`hv=hc//lamda`
`=(6.626xx10^(-34)Jsxx3.0xx10^(8)ms^(-1))/(300xx10^(-9)m)`
`=6.626xx10^(-19)J`
The energy of one mole of photons
`=6.626xx10^(-19)Jxx6.022xx10^(23)mol^(-1)`
`=3.99xx10^(5)Jmol^(-1)`
The minimum energy needed to remove one mole of electrons from sodium
`=(3.99-1.68)10^(5)Jmol^(-1)`
`=2.31xx10^(5)Jmol^(-1)`
The minimum energy for one electron
`=(2.31xx10^(5)Jmol^(-1))/(6.022xx10^(23)"electrons "mol^(-1))`
`=3.84xx10^(-19)J`
This corresponds to the wavelength
`:.lamda=(hc)/(E)`
`=(6.626xx10^(-34)Jsxx3.0xx10^(8)ms^(-1))/(3.84xx10^(-19)J)`
=517nm
(This corresponds to green light)