Use the formulas:
E=hnuE=hν, where EE is energy (J), hh is Planck's constant (Js), and nuν is the frequency (Hz).
and
c=lambdanuc=λν, where cc is the speed of light in a vacuum (m/s), lambdaλ is the length of a wavelength (m), and nuν is the frequency (Hz).
Solving the second formula for nuν, we get nu=c/lambdaν=cλ
Combining these formulas, we get:
E=(hc)/lambdaE=hcλ
For the first question, we are given that lambda=40λ=40 nm or 40*10^-940⋅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^-18E=(6.626⋅10−34)(3⋅108)40⋅10−9=4.9695⋅10−18
E=5.0*10^-18E=5.0⋅10−18 "J"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^-940⋅10−9 m:
E=(4.9695*10^-18)*(6.02*10^23)=2.99164*10^6E=(4.9695⋅10−18)⋅(6.02⋅1023)=2.99164⋅106
E=3.0*10^6E=3.0⋅106 "J/mol"J/mol with proper significant figures
