Question

1. ultraviolet radiation has a frequency of 8.2x10¹⁵ hz. determine its wavelength.

Explanation:

Step1: Recall the wave - speed formula

The speed of light $c$ is related to frequency $f$ and wavelength $\lambda$ by the formula $c = f\lambda$, where $c=3\times 10^{8}\ m/s$ (speed of light in vacuum) and $f = 8.2\times 10^{15}\ Hz$. We need to solve for $\lambda$.

Step2: Rearrange the formula to solve for wavelength

Rearranging $c = f\lambda$ gives $\lambda=\frac{c}{f}$.

Step3: Substitute the values of $c$ and $f$

Substitute $c = 3\times 10^{8}\ m/s$ and $f = 8.2\times 10^{15}\ Hz$ into the formula: $\lambda=\frac{3\times 10^{8}}{8.2\times 10^{15}}$.
Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $\lambda=\frac{3}{8.2}\times10^{8 - 15}$.
$\frac{3}{8.2}\approx0.366$ and $10^{8 - 15}=10^{-7}$. So $\lambda\approx3.66\times 10^{-8}\ m$.

Answer:

$3.66\times 10^{-8}\ m$