Question

A source containing a mixture of hydrogen and deuterium atoms emits light at two wavelengths whose mean is 513 nm and whose separation is 0.139 nm. Find the minimum number of lines needed in a diffraction grating that can resolve these lines in the first order.

Answer 1

Minimum number of lines, N = 3690.64

Step-by-step explanation:

Mean of wavelengths,
`\lambda_(avg)=513\ nm=513* 10^(-9)\ m`

Smallest resolvable wavelength difference,
`\Delta \lambda=0.139\ nm=0.139* 10^(-9)\ m`

Resolution of diffraction grating is given by :

`(\lambda_(avg))/(\Delta \lambda)=mN`

For first order, m = 1

N is the minimum number of lines

`N=(\lambda_(avg))/(\Delta \lambda)`

`N=(513* 10^(-9))/(0.139* 10^(-9))`

N = 3690.64

Hence, the minimum number of lines needed in a diffraction grating that can resolve these lines in the first order is 3690.64. Hence, this is required solution.