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

Explanation:

Step1: Identify the formula and given values

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

Step2: Rearrange the formula to solve for \( x \)

Starting with \( y=\frac{3\times10^{8}}{x} \), we can multiply both sides by \( x \) to get \( yx=3\times 10^{8} \), then divide both sides by \( y \) to obtain \( x=\frac{3\times 10^{8}}{y} \).

Step3: Substitute the given value of \( y \) into the formula

Substitute \( y = 3\times10^{18} \) into \( x=\frac{3\times 10^{8}}{y} \):

$$ x=\frac{3\times 10^{8}}{3\times 10^{18}} $$

Step4: Simplify the expression

When dividing numbers in scientific notation, we divide the coefficients and subtract the exponents of 10. The coefficient \( \frac{3}{3} = 1 \), and for the exponents of 10, \( 8 - 18=- 10 \). So we have \( x = 1\times10^{-10}\text{ m} \).

Answer:

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