Exercise 36.32 Part A Different isotopes of the same element emit light at sligh

Question

Exercise 36.32 Part A 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 What minimum number of slits is required to resolve these two wavelengths in second order? N= 11215 N-1215 slits Submit My Answers Give Up Incorrect; Try Again; 2 attempts remaining Part 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. 0, = 10.006564 Submit My Answers Give Up Incorrect; Try Again; 2 attempts remaining

Explanation / Answer

from rayleign criterion R = L/dL

where dL = 656.45 - 656.27 = 0.18

R = (656.27)/0.18 * 0.5

R = 1823

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use d sin theta = mL

d = 1/50000

d = 20 um

so

sin theta = 2 * 656.45*10^-9/(20 *10^-6)

sin theta = 0.0656

theta = 3.756 deg

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sin theta = 2 * 656.27*10^-9/(20*10^-6)

theta = 3.7628 deg

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angular separation dtheta = 3.7628 - 3.756 = 0.0068 deg

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