A source containing a mixture of hydrogen and deuterium atoms emits light at two wavelengths whose mean is 540 nm and whose separation is 0.170 nm. Find the minimum number of lines needed in a diffraction grating that can resolve these lines in the first order.

N=3176.5rulling

Explanation:

We were told that the source containing a mixture of hydrogen and deuterium atoms emits light with

wavelengths whose mean is 540 nm

Then λ= 540 nm, but we need to convert to metre which = (540× 10⁻⁹m)

Also whose separation is 0.170 nm, which mean the difference between the wavelength is 0.170 nm then

Δ λ = 0.170 nm the we convert to metre we have. Δλ= 0.170 nm= (0.170×10⁻⁹m)

the formular below can be used to can be used to calculate our minimum number of lines

N= λ /(m Δλ)

Where N is number of fillings i.e number of lines

λ= wavelength

Δλ= difference in wavelength

m=1

Then if we substitute the values we have

,N= (540× 10⁻⁹ m)/[(1)*(0.170× 10⁻⁹m)]

N =3176.5rulling

Therefore, minimum number of lines = =3176.5rulling