Question

A microwave oven operates at 2.50 GHz. What is the wavelength of the radiation produced by this appliance?

Answer 1

`"0.120 m"`

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

`nu` - the frequency of the electromagnetic wave
`lamda` - its wavelength
`c` - the speed of light in a vaccuum, usually given as `3 * 10^8"m s"^(-1)`

In your case, the frequency of the wave is said to be equal to `"2.50 GHz"`. Now, hertz is defined as one cycle per second. Your electromagnetic wave has a frequency of

`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 `2.50 * 10^9` complete cycles. You can thus rewrite the given frequency as

`nu = 2.50 * 10^9"s"^(-1)`

Rearrange the above equation to solve for `lamda`

`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.