The energy required to ionize sodium is 496 kJ /mol. What minimum frequency of light is required to ionize sodium?
1 Answer
Explanation:
Your strategy here will be to
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use Avogadro's number to find the energy needed to ionize one atom of sodium
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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
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
Plug in your values and solve for
#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