Question

the inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y
$y = \frac{3 \times 10^8}{x}$
what are the wavelengths for x - rays with frequency $3 \times 10^{18}$?
options:
$1 \times 10^{-10}$ m
$3 \times 10^{26}$ m
$3 \times 10^{-10}$ m
$9 \times 10^{26}$ m

Explanation:

Step1: Identify the formula and given values

The inverse variation equation is \( y=\frac{3\times10^{8}}{x} \), where \( y \) is the frequency and \( x \) is the wavelength. We are given \( y = 3\times10^{18} \).

Step2: Substitute the given frequency into the equation

Substitute \( y = 3\times10^{18} \) into \( y=\frac{3\times10^{8}}{x} \), we get \( 3\times10^{18}=\frac{3\times10^{8}}{x} \).

Step3: Solve for \( x \)

First, multiply both sides by \( x \): \( 3\times10^{18}x = 3\times10^{8} \).
Then, divide both sides by \( 3\times10^{18} \): \( x=\frac{3\times10^{8}}{3\times10^{18}} \).
Simplify the right - hand side: Using the rule of exponents \( \frac{a^{m}}{a^{n}}=a^{m - n} \), we have \( x=\frac{3}{3}\times10^{8-18}=1\times10^{- 10} \) meters.

Answer:

\( 1\times10^{-10}\text{ m} \)