Question

How much energy does a quantum of electromagnetic energy at 400 nm contain? How much more or less is this than a quantum of electromagnetic energy at 2.7 μm? 

Answer 1

The energy can be found from the relation $E=h\nu=hc/\lambda$, where λ is the wavelength of the quantum. After substitution, we find for λ = 400 nm the energy as

$E_1=\cfrac{hc}{\lambda}=\frac{(6.626\times 10^{-34}Js)(3\times 10^8m/s)}{400\times 10^{-9}m} \\ E_1=4.9695\times 10^{-19}J$

Then for the second quantum, we calculate the energy for λ = 2.7 μm:

$E_2=\cfrac{hc}{\lambda}=\frac{(6.626\times 10^{-34}Js)(3\times 10^8m/s)}{2.7\times 10^{-6}m} \\ E_2=7.3622\times 10^{-20}J$

The relation between the energies is

$E_2/E_1=\cfrac{7.3622\times 10^{-20}J}{4.9695\times 10^{-19}J}=0.1481$

In conclusion, a quantum of electromagnetic energy at 400 nm contains about 4.9695 X 10^-19 J of energy, and a quantum of electromagnetic energy at 2.7 μm contains less energy (about 14.81% of the first energy E₁) than the first quantum mentioned.

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.