Question

the inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y. y = 3×10^8/x. what are the wavelengths for x - rays with frequency 3×10^18? 1×10^-10 m 3×10^-10 m 3×10^26 m

Explanation:

Step1: Recall wave - speed formula

The speed of light $c = 3\times10^{8}\ m/s$ and the relationship between the speed of light $c$, frequency $f$ and wavelength $\lambda$ is $c = f\lambda$. We want to find $\lambda$, so $\lambda=\frac{c}{f}$.

Step2: Substitute values

Given $c = 3\times10^{8}\ m/s$ and $f = 3\times10^{18}\ Hz$, then $\lambda=\frac{3\times10^{8}}{3\times10^{18}}$.

Step3: Use exponent rules

When dividing numbers in scientific - notation $a\times10^{m}\div b\times10^{n}=\frac{a}{b}\times10^{m - n}$. Here, $\frac{3}{3}\times10^{8-18}=1\times10^{- 10}\ m$.

Answer:

$1\times10^{-10}\ m$