In order to answer this question, we'll need to use two equations:
#E = h*ν#, where E is the energy of a photon, #h# is Planck's constant (#6.626*10^-34"J s"#), and #ν# is frequency (in #"Hz"#).
#c = λ*ν#, where #c# is the speed of light (#3.0*10^8"m/s"#), #λ# is wavelength, and #ν# is frequency (in #"Hz"#) again.
To solve for frequency, we just need to plug in the energy of the photon into the first equation:
#E = h*ν#
#15.0 * 10^-16 J = 6.626*10^-34"J s" * ν#
#ν = (15.0 * 10^-16 J)/(6.626*10^-34 "J s") = 2.26 * 10^18"Hz"#
To solve for wavelength, we need to plug in frequency into the second equation.
#c = λ*ν#
#3.0*10^8"m/s" = λ*(2.26*10^18"Hz")#
#λ = (3.0*10^8"m/s")/(2.26 * 10^18"Hz") = 1.33 * 10^-10"m"#
Since the question asks for an answer in nanometers, which is #1*10^-9m#, we need to convert our answer from meters into nanometers.
#1.33 * 10^-10"m" = 1.33 * 10^-1"nm"#
