Use the formulas:
#E=hnu#, where #E# is energy (J), #h# is Planck's constant (Js), and #nu# is the frequency (Hz).
and
#c=lambdanu#, where #c# is the speed of light in a vacuum (m/s), #lambda# is the length of a wavelength (m), and #nu# is the frequency (Hz).
Solving the second formula for #nu#, we get #nu=c/lambda#
Combining these formulas, we get:
#E=(hc)/lambda#
For the first question, we are given that #lambda=40# nm or #40*10^-9# m. By substituting into the above formula, we get:
#E=((6.626*10^-34)(3*10^8))/(40*10^-9)=4.9695*10^-18#
#E=5.0*10^-18# #"J"# with proper significant figures
For the second question, we can use our answer for the first question (the amount of energy for a single photon) and Avogadro's number to find the the amount of energy in a mole of photons with wavelength of #40*10^-9# m:
#E=(4.9695*10^-18)*(6.02*10^23)=2.99164*10^6#
#E=3.0*10^6# #"J/mol"# with proper significant figures
