What is the wavelength of an X-ray whose frequency is 1.192 x 1018 Hz? c=𝜆𝜈

Answer 1

Use the equation c = λ x v

where c = speed of light (3.0 x 10⁸ m/s)

v = frequency (can be expressed in either Hz or s^-1, but 1 Hz = 1 s^-1)

and λ = wavelength (typically expressed in nanometers)

Rewrite the expression to solve for λ:

λ = c / v

Substitute in your known values for c and v and solve for λ:

λ = (3.0 x 10⁸ m/s) / (1.192 x 10¹⁸ s^-1) = 2.5168 x 10^-10 meters

(Im expressing your frequency in inverse seconds here so you can see that the seconds unit in the numerator and denominator cancel out and leave you with meters, ie the si unit for wavelength)

I am going to express your wavelength in nanometers because wavelength is typically expressed in that unit, since it is an easier number to work with. I know the problem doesn't ask you to convert to nm, but I am going to show you how to because it is a step you should know how to do.

1 meter = 1 x 10⁹ nanometers (use this information to write a conversion factor to convert to nm)

2.5168 x 10^-10 meters ( 1 x 10⁹ nanometers / 1 meter) = 0.25168 nm

Hint: If you are unsure of if your answer is correct, substitute the value you got for wavelength back into the original equation (c = λv), if you multiply your answer (in meters) by the given frequency in the problem, the resulting number should be approximately equal to the speed of light (3.0 x 10⁸ m/s).