### Phys 4910 Spectroscopy Spring 2014 Assignment 3

1. A grating with 1500 lines per mm is described as having a blaze angle of “5500 Å in 1st order. What is the angle of the ruled grating surface relative to the flat substrate? (Be careful, you might want to look at the section in your General Physics book which talks about flat mirror.)
2. One of the problems with gratings is that of overlapping orders. Suppose I have a grating with 400 lines per mm. Assuming your detector can respond to radiation in the optical (near uv, light, and near IR) range of the spectrum, from 320 nm to 860 nm, and that the incident beam is normal to the grating.
1. What is the range of angles covered by the optical range in 1 st order?
2. What is the range of angles covered by the optical range in 2 nd order?
3. Radiation is detected at an angle of 32° . What is its wavelength?
4. Radiation is detected at an angle of 18° . What is its wavelength?
3. For the Bohr atom
1. find the speed of the electron in the lowest orbit of hydrogen
2. find the time the electron takes of make one orbit
3. how does this compare with the frequency of light?
4. Because of the reduced mass the wavelength of light emitted by different isotopes of the same element are slightly different (the isotope shift)
1. Using the Bohr model, calculate the isotope shift between hydrogen and deuterium for the four visible lines of the hydrogen spectrum, that is the Balmer series.
2. What is the minimum resolving power of a spectrometer which is able to detect the isotope shift?
5. The size of a Bohr atom can be defined as the diameter of the orbit of the electron with the highest value of n, call it nmax
1. Find the diameter of the hydrogen atom, for which nmax = 1.
2. Find the diameter of the helium atom, for which nmax = 1.
3. Find the diameter of the uranium atom, for which nmax = 7.
4. Comment on the results. (Note: for part 2 of this question look up the details of Rutherford's experiment to show that particles are in fact helium nuclei.)