i have an iron gas that has two strong emmision lines at landa1=140.903 nm and l

Question

i have an iron gas that has two strong emmision lines at landa1=140.903 nm and landa2 = 140.992nm when viewed through a grating spectroscope.  .if the diffraction grating has a split seperation of .20mm and the grating is 1.0m from the screen, then (a) find the distance between these these two emmission lines in the 2nd order on the screen. (hint: find the angles that landa1 and landa2 make with the central axis). (b) find the number of slits, N, needed to just resolve these lines. please show all your work. thanks

Explanation / Answer

a) dsin(theta) = 2*lamda

theta = arcsin(2*lambda/d)

theta1 = arcsin(2*lambda1/d) = arcsin(2*140.903*10^-9/(0.20*10^-3))=0.0807314991 degrees

theta2 = arcsin(2*lambda2/d) = arcsin(2*140.992*10^-9/(0.20*10^-3))=0.0807824924 degrees

distance = D*[tan(theta2)-tan(theta1)] = 1*(tan(0.0807824924 degrees)-tan(0.0807314991 degrees)) = 8.9000275 E-7 m = 890.00275 nm

b)R = lambda/delta lambda = 140.903/(140.992-140.903) = 1583.18

and R = m*N

==> 1583.18 = 2*N

==> N = 791.58

==> N = 792

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