Chemistry · Structure Of Atom · NEET
Wavenumber (nu-bar) = 1 / wavelength (lambda). That is all. You take the wavelength and flip it. Example: if lambda = 500 nm = 500 x 10^-9 m, then nu-bar = 1 / (500 x 10^-9) = 2 x 10^6 m^-1. Do NOT put speed of light in this formula. c/lambda gives frequency, not wavenumber.
Since wavenumber = 1/wavelength, its unit is the reciprocal of length. The SI unit is m^-1 (per metre). But in real spectroscopy and in most NEET numericals the unit cm^-1 (per centimetre) is used because it gives smaller, easier numbers. Remember: cm^-1 is NOT an SI unit, but it is the most common one. To go from m^-1 to cm^-1, divide by 100.
Wavenumber = 1/lambda. Frequency = c/lambda. These two are different and NTA loves to swap them. Wavenumber only needs the wavelength. Frequency needs the wavelength AND the speed of light c. If you accidentally multiply 1/lambda by c, you get frequency, not wavenumber.
Both tell you 'how many waves', but in different ways. Frequency (nu) = number of waves passing a point per SECOND, unit Hz or s^-1, formula c/lambda. Wavenumber (nu-bar) = number of waves in one unit of LENGTH, unit cm^-1 or m^-1, formula 1/lambda. Simple link: nu-bar = nu / c, so wavenumber = frequency divided by speed of light.
Step 1: write wavelength in the length unit you want the answer in (metre for m^-1, centimetre for cm^-1). Step 2: take 1 divided by that number. Example: lambda = 5800 angstrom = 5800 x 10^-8 cm, so nu-bar = 1/(5800 x 10^-8) = 1.72 x 10^4 cm^-1. Watch your unit conversions - that is where most marks are lost.
Because in spectroscopy the numbers in m^-1 are huge (like 10^6). Using cm^-1 makes them 100 times smaller and easier to read and compare. For example, a wavenumber of 1.72 x 10^6 m^-1 becomes 1.72 x 10^4 cm^-1. Both are correct - cm^-1 is just more practical for lab and exam work.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is the number of full waves packed into one unit of length (per metre or per centimetre). A larger wavenumber means shorter waves squeezed closer together.
nu-bar = nu / c, that is wavenumber equals frequency divided by the speed of light. This is because nu = c/lambda and nu-bar = 1/lambda.
Inversely. Since nu-bar = 1/lambda, a bigger wavelength gives a smaller wavenumber, and a smaller wavelength gives a bigger wavenumber.
m^-1 (per metre) is the SI unit. But cm^-1 (per centimetre) is more commonly used in spectroscopy and NEET numericals, even though it is not SI.
Wavenumber depends on wavelength, and wavelength changes with the medium. In NEET numericals we usually work in vacuum/air where you just use nu-bar = 1/lambda.
