Grate Register
Posted in Garden Antiques on 08/01/2010 02:28 pm by adminWhat is the position of the second member of the Paschen series?
Light from a hydrogen discharge passes through a diffraction grating and registers on a detector 1.5 m behind the grating. The m=1 diffraction of the first member of the Paschen series is located 60.7 cm from the central maximum. What is the position of the second member of the Paschen series?
I know: wavelength = 91.18nanometers / (1/m^2 - 1/n^2) and that theta_m = (m*wavelength) / (d)
where m is an integer 1,2,3... and d is the slit seperation.
Not sure if those are the formulas to use... The problem basically wants me to relate the paschen series to the formulas used to calculate a diffraction grating. Any ideas?
The Paschen series is the set of orbit changes and associated energies and wavelengths associated with transition between the 3rd hydrogen orbit and the higher-energy orbits beyond it.
Based on the formula you cite,
The 1st Paschen transition, 3-4, has lambda = 1875.7 nm.
The 2nd Paschen transition, 3-5, has lambda = 1282.2 nm.
First we solve for grating spacing d given the 1st wavelength and the observed values of y (location of m=1 peak) and D (detector distance).
Θ = arctan(y/D) = 0.384522880645716 rad
d = m*lambda/sin(Θ) = 5.00030789671322E-06 m
Then we solve for y with the 2nd wavelength:
Θ = arcsin(m*lambda/d) = 0.259320892072004 rad
y = D*tan(Θ) = 0.397941759430815 m
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