Question

The energy required to ionize sodium is 496 kJ /mol. What minimum frequency of light is required to ionize sodium?

Answer 1

`1.24 * 10^(15)"Hz"`

Explanation:

Your strategy here will be to

• use Avogadro's number to find the energy needed to ionize one atom of sodium

• use the Planck - Einstein equation to find the frequency of light that corresponds to that specific energy

So, you know that the energy needed to ionize sodium is equal to `"496 kJ/mol"`. As you know, one mole of any element contains exactly `6.022 * 10^(23)` atoms of that element - this is known as Avogadro's number.

In your case, the energy needed to ionize one atom of sodium will be equal to

`496 color(red)(cancel(color(black)("kJ")))/color(red)(cancel(color(black)("mol"))) * (10^3 "J")/(1 color(red)(cancel(color(black)("kJ")))) * (1color(red)(cancel(color(black)("mol"))))/(6.022 * 10^(23)"atoms") = 8.236 * 10^(-19)"J/atom"`

The relationship that exists between energy and frequency is described by the Planck - Einstein equation

`color(blue)(E = h * nu)" "`, where

`E` - the energy of the wave
`h` - Planck's constant, equal to `6.626 * 10^(-34)"J s"`
`nu` - the frequency of the wave

Plug in your values and solve for `nu`, the frequency of light needed to ionize a sodium atom

`E = h * nu implies nu = E/h`

`nu = (8.236 * 10^(-19) color(red)(cancel(color(black)("J"))))/(6.626 * 10^(-34)color(red)(cancel(color(black)("J"))) "s") = 1.243 * 10^15"s"^(-1)`

Since you have

`"1 Hz" = "1 s"^(-1)`

you can say that the answer will be

`nu = color(green)(1.24 * 10^(15)"Hz") ->` rounded to three sig figs