A beam of electromagnetic radiation has a wavenumber of 40000 ~cm ⁻¹ . The wavelength of this radiation in nanometers (nm) is ________.

Step-by-step solution

The relationship between wavenumber ( ) and wavelength ( ) is given by: = 1 Given = 40000 ~cm ⁻¹ , we have: = 1 40000 ~cm = 2.5 10⁻⁵ ~cm To convert centimeters to nanometers, we use the conversion factors 1 ~cm = 10⁻² ~m and 1 ~nm = 10⁻⁹ ~m : = 2.5 10⁻⁵ 10⁻² ~m = 2.5 10⁻⁷ ~m = 2.5 10⁻⁷ 10⁻⁹ ~nm = 250 ~nm Answer: 250