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QUESTION

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

1.24 * 10^(15)"Hz"

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 - , 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