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

Answer:

Minimum number of lines, N = 3690.64

Explanation:

Mean of wavelengths, $\lambda_{avg}=513\ nm=513\times 10^{-9}\ m$

Smallest resolvable wavelength difference, $\Delta \lambda=0.139\ nm=0.139\times 10^{-9}\ m$

Resolution of diffraction grating is given by :

$\dfrac{\lambda_{avg}}{\Delta \lambda}=mN$

For first order, m = 1

N is the minimum number of lines

$N=\dfrac{\lambda_{avg}}{\Delta \lambda}$

$N=\dfrac{513\times 10^{-9}}{0.139\times 10^{-9}}$

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.