When electromagnetic radiation of wavelength 300 nm falls on the surface of sodium, electrons are emitted with kinetic energy of `1.68 xx 10^(5) J "ml"^(-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)/(lambda) = (6.626 xx 10^(-34) Js xx 3.0 xx 10^(8)ms^(-1))/(300 xx 10^(-9)m)`
The energy of one mole of photons
`= 6.626 xx 10^(-19)J xx 6.022 xx 10^(23) mol^(-1) = 3.99 xx 10^(5) J mol^(-1)`
The minimum energy needed to remove one mole of electron from sodium.
`= (3.99 - 1.68) 10^(5)J mol^(-1) = 2.31 xx 10^(5) J mol^(-1)`
The minimum energy for one electron
`= (2.31 xx 10^(5) J mol^(-1))/(6.022 xx 10^(23) "electrons" mol^(-1)) = 3.84 xx 10^(-19)J`
This corresponds of the wavelength
`:. lambda = (hc)/(E) = (6.626 xx 10^(-34)Js xx 3.0 xx 10^(8)ms^(-1))/(3.84 xx 10^(-19)J) = 517 nm`
This wavelength corresponds to green colour in visible spectrum.