What is the energy in electron volts of X-rays that have a frequency of #3.00 * 10^16# #Hz#?
1 Answer
Explanation:
The first thing to do here is use the Planck - Einstein Relation to calculate the energy of an X-Ray photon that has a frequency of
According to the Planck - Einstein Relation, the energy of a photon is proportional to its frequency
#color(blue)(|bar(ul(color(white)(a/a)E = h * nucolor(white)(a/a)|)))#
Here
Before plugging in your value for the frequency of the photon, don't forget to use the fact that
#E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * 3.00 * 10^(16)color(red)(cancel(color(black)("s"^(-1))))#
#E = 1.988 * 10^(-17)"J"#
Now, an electronvolt,
#color(blue)(|bar(ul(color(white)(a/a)"1 eV" = 1.6022 * 10^(-19)"J"color(white)(a/a)|)))#
Use the definition of an electronvolt as a conversion factor to convert the energy of your photon from joules to eV
#1.988 * 10^(-17)color(red)(cancel(color(black)("J"))) * "1 eV"/(1.6022 * 10^(-19)color(red)(cancel(color(black)("J")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("124 eV")color(white)(a/a)|)))#
The answer is rounded to three sig figs.