A microwave oven operates at 2.50 GHz. What is the wavelength of the radiation produced by this appliance?
1 Answer
Explanation:
What you need to know here is that frequency and wavelength have an inverse relationship as described by the equation
#color(blue)(|bar(ul(color(white)(a/a)nu * lamda = c color(white)(a/a)|)))#
Here
In your case, the frequency of the wave is said to be equal to
#2.50 color(red)(cancel(color(black)("GHz"))) * (10^9"Hz")/(1color(red)(cancel(color(black)("GHz")))) = 2.50 * 10^9"Hz"#
which means that in one second it covers
#nu = 2.50 * 10^9"s"^(-1)#
Rearrange the above equation to solve for
#nu * lamda = c implies lamda = c/(nu)#
Plug in your value to find
#lamda = (3 * 10^8"m" color(red)(cancel(color(black)("s"^(-1)))))/(2.50 * 10^9color(red)(cancel(color(black)("s"^(-1))))) = color(green)(|bar(ul(color(white)(a/a)color(black)("0.120 m")color(white)(a/a)|)))#
The answer is rounded to three sig figs, the number of sig figs you have for the frequency of the electromagnetic wave.