Question

what is the wavelength of electromagnetic radiation which has a frequency of 4.464 x 10^{14} s^{-1}?
6.716 x 10^{-7} nm
1.489 x 10^{-6} m
1.338 x 10^{23} m
7.472 x 10^{-15} nm
671.6 nm

Explanation:

Step1: Recall the formula for the speed of light

The speed of light \(c = \lambda
u\), where \(c = 3\times10^{8}\space m/s\) (speed of light in vacuum), \(\lambda\) is the wavelength and \(
u\) is the frequency. We need to solve for \(\lambda\), so \(\lambda=\frac{c}{
u}\).

Step2: Substitute the values

Given \(
u = 4.464\times 10^{14}\space s^{-1}\) and \(c = 3\times 10^{8}\space m/s\).
\(\lambda=\frac{3\times 10^{8}}{4.464\times 10^{14}}\space m\)

$$
LATEXBLOCK0
$$

Since \(1\space m=10^{9}\space nm\), then \(\lambda=6.716\times10^{-7}\times10^{9}\space nm = 671.6\space nm\)

Answer:

671.6 nm