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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.

User Aki
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1 Answer

4 votes

Answer:

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.

User Arowell
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7.3k points
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