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)"Js"xx3.0xx10^(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)j "mol"^(-1)`
The minimum energy needed to remove a mole of electrons from sodium
`(3.99-1.68)10^(5)J "mol"^(-1)`
= `2.31xx10^(5)J "mol"^(-1)`
The minimum energy for one electron
`=(2.31xx10^(5)J "mol"^(-1))/(6.022xx10^(23)"electrons mol "^(-1))=3.84"10"^(-19)J`
This corresponds to the wavelength
`thereforelamda=(hc)/(E)`
`=(6.626xx10^(-34)Jsxx3.0xx10^(8)"ms"^(-1))/(3.84xx10^(-19)J)=517"nm"`
(This corresponds to green light)