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.

When electromagnetic radiation of wavelength 300 nm falls on the surfa

1.	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.
Answer» 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.

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