Question

Calculate the wavelength of a wave that has the frequency of 7.32 x 20^14 Hz. Express your answer in nanometers and 3 dog figs.

A) 4.100 nm
B) 4.1 nm
C) 4.10 nm
D) 4.0 nm

Answer 1

The wavelength of a wave with a frequency of 7.32 x 10¹⁴ Hz is calculated using the formula λ = c/f. When converted to nanometers and rounded to three significant figures, the wavelength is approximately 410 nm, corresponding to option B) 4.1 nm.

Step-by-step explanation:

To calculate the wavelength of a wave with a given frequency, you can use the formula c = λf, where c is the speed of light in a vacuum (approximately 3.00 x 108 m/s), λ is the wavelength, and f is the frequency. Given the frequency of 7.32 x 1014 Hz, we can rearrange the formula to solve for the wavelength λ: λ = c/f.

Plugging in the given values, we get λ = (3.00 x 108 m/s) / (7.32 x 1014 Hz) = approximately 4.09836 x 10−7 meters. To express this in nanometers (1 nm = 10−9 m), we multiply the result by 109: 4.09836 x 10−7 m x 109 nm/m = 409.836 nm. When expressed to three significant figures, the wavelength is 410 nm, which aligns with option B) 4.1 nm.