Different isotopes of the same element emit light at slightly different waveleng

Question

Different isotopes of the same element emit light at slightly different wavelengths. A wavelength in the emission spectrum of a hydrogen atom is 656.45 nm; for deuterium, the corresponding wavelength is 656.27 nm.
a) What minimum number of slits is required to resolve these two wavelengths in second order?
b) If the grating has 500.00 slits/mm, find the angle of the wavelength of 656.45 nm in the second order.
Express your answer using six significant figures.
c) If the grating has 500.00 slits/mm, find the angle of the wavelength of 656.27 nm in the second order.
Express your answer using six significant figures.

Explanation / Answer

d sin (theta m) = m lamda d is spacing, we have 1/spacing m is order, we have second order sin (theta 2) = 2 lamda / d d = mm/500 = microns/.5 = 2 microns part b) lamda = 0.65645 microns sin theta 2 = 2*0.65645/2 = 0.65645 theta 2 = 41.0297 deg part c) lamda = 0.65627 microns theta 2 = 41.0160 deg

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