A rigid quantum rotator

The rotation of micro-objects around a motionless axis was analyzed in Section 7.5.3. The orbital motion of an electron was used as an example. It was found that in this case the rotational energy can accept only discrete values defined by eq. (7.5.26). Since potential energy in free rotation is accepted to be equal to zero, the total energy is kinetic. One of the important characteristics of such movement is the rotational constant B  

The 4 value is called the reduced moment of inertia ficB. The quantum number in the optical rotational spectroscopy is defined by another letter (letter j instead of /) Therefore the rotational energy can be written as 

It is easy to calculate the energy distance between rotational levels. Naturally, 

The absolute distance between levels increases at increasing j however, the relative values, AE/E vice versa, decrease. This corresponds to the Bohr correspondence principle. 

A beam of neutrons is thermolyzed by a room temperature moderator (T = 300 K) in a nuclear reactor. It then passes a special collimator in a hole in the reactor wall and falls on a graphite single crystal. A diffracted plane of the first order = 1 from the graphite base with interplanar spacing d = 33.5 pm was measured at an angle 26 = 25.5°. Find neutron wavelength A, its velocity n and mass m. 

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