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 } )?

( 3 \times 10 ^ { - 10 } m )( 1 \times 10 ^ { - 10 } m )( 3 \times 10 ^ { 26 } m )( 9 \times 10 ^ { 26 } m )

Explanation:

Step1: Substitute the value of \(y\) into the equation

Given \(y=\frac{3\times10^{8}}{x}\) and \(y = 3\times10^{18}\), we substitute \(y\) into the equation: \(3\times10^{18}=\frac{3\times10^{8}}{x}\)

Step2: Solve for \(x\)

Cross - multiply: \(3\times10^{18}\times x=3\times10^{8}\)
Then \(x=\frac{3\times10^{8}}{3\times10^{18}}\)
Using the rule \(\frac{a^{m}}{a^{n}}=a^{m - n}\), we have \(x = 10^{8-18}=10^{- 10}\)

Answer:

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