Question

The binding energy of electrons in a metal is 192 kj/mol . part a find the threshold frequency of the metal.

Answer 1

To calculate the threshold frequency of the metal we use the formula,

`E=h\\u_(o)`

Also,
`\\u_(o)=(E)/(h)`

Here, E is the energy of electron per atom, h is plank constant.

Given, binding energy of electron
`E=192kJ/mol` or for one electron,
`E=(192 kJ/mol)/(N)`, here N is the Avogadro constant and its value is
`6.023*10^(23)`, so
`E=(192*10^3 J)/(6.023*10^(23))=3.19*10^(-19)  J` and plank constant,
`h=6.626*10^(-34) Js`

Substituting these values in above relation we get,

`\\u _(o) =(3.19 *10^(-19J) )/(6.626 * 10^(-34)Js ) =4.81* 10^(14) Hz`.

Thus, the threshold frequency of the metal is
`4.81 * 10^(14) Hz`.