Question

Calculate the frequency and wave number of microwaves with a wavelength of 4 × 107 nm.

Answer 1

Frequency = $7.5 \times 10^9$ Hz Wave number = $25$ m$^{-1}$

Answer 2

1. Convert the given wavelength from nanometers (nm) to meters (m) using the conversion factor $1 \text{ nm} = 10^{-9} \text{ m}$.

2. Use the relationship between the speed of light ($c$), frequency ($\nu$), and wavelength ($\lambda$), $c = \nu \lambda$, to calculate the frequency $\nu = c/\lambda$. Use $c = 3 \times 10^8 \text{ m/s}$.

3. Calculate the wave number ($\bar{\nu}$) as the reciprocal of the wavelength ($\lambda$), $\bar{\nu} = 1/\lambda$.