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

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