Question #6f835
1 Answer
Explanation:
The energy of a photon is directly proportional to its frequency as given by the Planck - Einstein relation
#color(purple)(bar(ul(|color(white)(a/a)color(black)(E = h * nu)color(white)(a/a)|)))#
Here
Notice that the problem provides you with the wavelength of the photon. In order to be able to calculate its energy, you will have to convert the given wavelength to frequency.
To do that, use the equation
#color(purple)(bar(ul(|color(white)(a/a)color(black)(lamda * nu = c)color(white)(a/a)|)))#
Here
Rearrange this equation to solve for
#lamda * nu = c implies nu = c/(lamda)#
Plug in your values to find
#nu = (3 * 10^8 color(red)(cancel(color(black)("m"))) * "s"^(-1))/(4.8color(red)(cancel(color(black)("m")))) = 6.25 * 10^7"s"^(-1)#
Now all you have to do is plug this into the Planck - Einstein equation and calculate the energy of the photon
#E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * 6.25 * 10^7color(red)(cancel(color(black)("s"^(-1)))) = color(green)(bar(ul(|color(white)(a/a)color(black)(4.1 * 10^(-26)"J")color(white)(a/a)|)))#
The answer is rounded to two sig figs.