Answer to Question #250043 in Mechanics | Relativity for John

Question #250043

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? 


1
Expert's answer
2021-10-13T09:08:22-0400

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


E1=hcλ=(6.626×1034Js)(3×108m/s)400×109mE1=4.9695×1019JE_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:


E2=hcλ=(6.626×1034Js)(3×108m/s)2.7×106mE2=7.3622×1020JE_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


E2/E1=7.3622×1020J4.9695×1019J=0.1481E_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.

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