The rotation spectrum of the HCl molecule has been observed in the far infrared, around 50 × 10−⁶ m. The spacing between successive lines in the spectrum corresponds to radiation of wavelength equal to 5 microns (1 μm = 10−⁶ m). Determine the frequency of the photon associated with this transition. A) 6 × 10¹⁴ Hz B) 6 × 10¹² Hz C) 6 × 10¹¹ Hz D) 6 × 10¹³ Hz E) 6 × 10¹⁰ Hz

Question

Quizplus · Accepted Answer

We can use the formula $c = \lambda
u$ where $c$ is the speed of light, $\lambda$ is the wavelength, and $
u$ is the frequency.

Rearranging the formula, we have $
u = \frac{c}{\lambda}$.

Substituting the given values, we get $
u = \frac{3	imes 10^8\; 	ext{m/s}}{5	imes 10^{-6}\; 	ext{m}} = 6	imes 10^{13}$ Hz.

Converting this to scientific notation we get $6	imes 10^{13}$ Hz, which matches option D.

The Rotation Spectrum of the HCl Molecule Has Been Observed