Question

What is the wavelength of electromagnetic radiation with a frequency of `7.1xx10^6` `"Hz"`?

Answer 1

The wavelength is `"42 m"`.

Explanation:

`c=lamda*nu`,

where:

`c` is the speed of light, `lamda`, pronounced lamda, is the wavelength, and `nu`, pronounced noo, is the frequency.

Given/Known

`c=3.00xx"10"^8" m/s"` to three significant figures

`nu=7.1xx"10"^6` `"Hz"` `larr` `"1 Hz = 1/s"`

Unknown

`lamda`

Solution

Rearrange the equation above to isolate `lamda`. Plug in the known values and solve.

`lamda=c/nu`

`lamda=(3.00xx10^8"m"/color(red)cancel(color(black)("s")))/(7.1""xx"10"^6/color(red)cancel(color(black)("s")))="42 m"` rounded to two significant figures

Answer 2

Wavelength times frequency = speed (of EM waves =speed of light)
Remember the unit conversion: `Hz=1//s`

Explanation:

`lambdaxxf=c`

Which can be reworked to:
`lambda=c/f`

`lambda=(3.0xx10^8mcancel(//s))/(7.1xx10^6cancel(//s))=0.42xx10^2m=42m`