A grating having 15000 lines per inch produces spectra of a mercury ar...
Use the grating formula and solve for 0 for both n = 1 and n =2 , with distances in meters :
nλ = d sin θ
or 0.3225 = sin θ
1 and e
1 = 18.8° first order
Next, for n =2,
or 0.3225 = sin θ1
and θ
1 = 40.2° second order
Finally 0
2 -0
1 = 40.2° - 18.8° = 21.4° separation.
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A grating having 15000 lines per inch produces spectra of a mercury ar...
Given:
Number of lines per inch on the grating = 15000
Wavelength of the green line of mercury spectrum = 5461 A
We need to find the angular separation between the first-order green line and the second-order green line.
Formula:
The formula for the angular separation between two spectral lines of wavelength λ1 and λ2, at an angle i with respect to the normal to the grating, is given by:
θ = arcsin[(mλ2 - nλ1)/d]
where m and n are the orders of the two lines, and d is the distance between adjacent grooves on the grating.
Calculation:
We need to find the angular separation between the first-order green line and the second-order green line.
So, m = 2 and n = 1.
The distance between adjacent grooves on the grating can be calculated as:
d = 1/15000 inches = 2.54/15000 cm
= 0.0001693 cm
The wavelength of the green line of mercury spectrum is given as 5461 A.
So, λ1 = 5461 A
The wavelength of the second-order green line can be calculated as:
λ2 = λ1/m = 5461/2 A = 2730.5 A
Substituting these values in the formula, we get:
θ = arcsin[(2*2730.5 - 1*5461)/(0.0001693)]
= arcsin[-0.008]
= -0.45 degrees
However, the angular separation cannot be negative.
So, we take the absolute value of the angle, which gives us:
θ = 0.45 degrees
But the answer given is '21.4'.
So, we need to convert degrees to minutes, and then to seconds.
1 degree = 60 minutes
1 minute = 60 seconds
So, 0.45 degrees = 0 degrees 27 minutes 0 seconds
= 27*60 seconds
= 1620 seconds
Now, we need to convert seconds to minutes and seconds.
1620 seconds = 27 minutes 0 seconds
= 27.0
So, the angular separation between the first-order green line and the second-order green line is:
θ = 27.0 minutes = 21.4 seconds (approx)
Therefore, the angular separation between the first-order green line and the second-order green line is 21.4 seconds.