Answer
$4.684\times10^{-4}m$ or $468400nm$
Work Step by Step
*Strategy: We would use the formula $$\lambda\times\nu=c$$
in which
$\lambda$ : wavelength of radiation
$\nu$: frequency of radiation
$c$: speed of light (we would take the speed of light in vacuum, which means $c\approx2.998\times10^8m/s$)
- Step 1: Find the known variables
The radiation has a frequency of $6.4\times10^{11}s^{-1}$, therefore $\nu=6.4\times10^{11}s^{-1}$
- Step 2: Do the calculation
The wavelength of radiation is
$\lambda=\frac{c}{\nu}=\frac{2.998\times10^8}{6.4\times10^{11}}\approx4.684\times10^{-4}m\approx468400nm$
