Question

given ( x = ) wavelength and ( y = ) frequency are inversely related, solve for the constant for the given type of radiation.
gamma-rays
frequency ( = 40 ) hz
wavelength ( = 300,000 )
( k = 12,000,000 )
( k = 40,000,000 )
( k = 0.0001 )
( k = 7,500 )

Explanation:

Step1: Recall inverse variation formula

For inverse variation, \( y=\frac{k}{x} \) (or \( x=\frac{k}{y} \)), so \( k = x \times y \).

Step2: Substitute values

Given \( x = 300000 \) (wavelength) and \( y = 40 \) (frequency), calculate \( k=300000\times40 \).
\( 300000\times40 = 12000000 \).

Answer:

\( k = 12,000,000 \) (the option with \( k = 12,000,000 \))