Microwaves range in wavelength from about 2.0 × 10^-2 cm to about 5.0 cm. What is the maximum energy in eV that a microwave may have? A) 0.025 meV B) 6.2 meV C) 2.5 eV D) 6.2 eV E) 0.62 meV

Question

Quizplus · Accepted Answer

The energy of a photon is given by E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength. Plugging in the maximum wavelength of 5.0 cm, we get E = (6.626 x 10^-34 J s) x (2.998 x 10^8 m/s) / (5.0 x 10^-2 m) = 3.98 x 10^-23 J. Converting to electron volts (eV), we divide by the elementary charge (1.602 x 10^-19 C/eV) to get 0.025 eV. However, the question asks for the maximum energy, so we need to use the minimum wavelength of 2.0 x 10^-2 cm instead. Plugging that in, we get E = (6.626 x 10^-34 J s) x (2.998 x 10^8 m/s) / (2.0 x 10^-2 m) = 9.94 x 10^-22 J, which is 6.2 meV when converted to eV. Therefore, the correct answer is B.

Microwaves Range in Wavelength from About 2