The hydrogen spectrum has a red line at 656 nm and a violet line at 434 nm. What
ID: 3895931 • Letter: T
Question
The hydrogen spectrum has a red line at 656 nm and a violet line at 434 nm. What is the angular separation between these two spectral lines obtained with a diffraction grating that has 4500 lines/cm? Solve for L. (tan theta= y/ L)
I don't understand how to find delta y in order to solve for L.
Here is what I have so far...
d= 2.22x10^ -6 theta r= 17.17degrees theta v= 11.27 and delta theta for the first order= 5.9
Second order theta r= 36.19 theta v= 23.02 delta theta= 13.17
My prof said to use the tan theta equation with both red and violet and that y(red) - y(violet) should= 1.75cm. No clue how to do this. Thanks for the help!!
Explanation / Answer
In interfreence or diffraction pattern
the needed equation is Y = mLR/d---------------1
and d sin theta = mL--------------------2
where L = wavelgnth
m = order = 1,2,3,4, ......... for brigth bands
m = 1.5, 2.5, 3.5, 4.5, ......for dark bands
R is the distance from slit to screen
Y = disatnce from central spot to nth order fringe or fringe width
so here now we apply, d =1/4500 = 2.22 um
tan theta 1 = 656nm /2.5nm = 0.262
theta 1 = 14.7 deg
tan theta2 = 434nm/2.5um = 0.173
theta 2 = 9.84
angular separation = 14.7-9.84 = 4.86 deg
iam pretty sure that angular separtion will not be measured in cm it will be measured in deg or radians so just check out woith your porfessor
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