Question

Question #2f4cc

Answer 1

Here's what I got.

Explanation:

For starters, you should know that the energy of a photon is directly proportional to its frequency as described by the Planck - Einstein equation

`color(blue)(ul(color(black)(E = h * nu)))`

Here

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

Your starting point here will be to figure out the energy of a single photon of green light, which covers frequencies that range from about `"520 THz"` to about `"609 THz"` `->` see this answer for more info on that.

Now, a terahertz is defined as

`"1 THz" = 10^(12)color(white)(.)"Hz" = 10^(12)color(white)(.)"s"^(-1)`

which means that the frequencies of green light range from

`5.20 * 10^(14)color(white)(.)"s"^(-1) " "` to `" " 6.09 * 10^(14)color(white)(.)"s"^(-1)`

Since you have a range of frequencies to work with, you can use the lowest frequency for green light to find the maximum number of photons that can generate that much energy and the highest frequency for green light to find the minimum number of photons that can generate that much energy.

So, you will have

`E_1 = 6.626 * 10^(-34)color(white)(.)"J"color(red)(cancel(color(black)("s"))) * 5.20 * 10^(14)color(red)(cancel(color(black)("s"^(-1)))) = 3.446 * 10^(-19)` `"J"`

`E_2 = 6.626 * 10^(-34)color(white)(.)"J"color(red)(cancel(color(black)("s"))) * 6.09 * 10^(14)color(red)(cancel(color(black)("s"^(-1)))) =4.035 * 10^(-19)` `"J"`

This means that the maximum number of photons that can generate that much energy is equal to

`10^(-17) color(red)(cancel(color(black)("J"))) * "1 photon"/(3.446 * 10^(-19)color(red)(cancel(color(black)("J")))) = color(darkgreen)(ul(color(black)(290)))`

Similarly, the minimum number of photons will be

`10^(-17)color(red)(cancel(color(black)("J"))) * "1 photon"/(4.035 * 10^(-19)color(red)(cancel(color(black)("J")))) = color(darkgreen)(ul(color(black)(250)))`

I'll leave the answers rounded to two sig figs.