Question

A nitric oxide molecule is in a rotational energy level described by rotational quantum number l=7. The rotational constant for NO is 1.695 cm-1.

what is the angular momentum?

how many different spatial orientations can this angular momentum vector take?

what is its rotational energy in Joules?

How much energy (in Joules) is required to excite it to the l=8 level?

What is its rotational frequency?

Answer #1

A NO molecule is in a rotational energy level described by rotational quantum number l =7

the rotational constant for NO = 1.695cm^{-1}

In rotation spectroscopy, for diatomic molecules like NO

solving the schrodinger equation for a rigid rotor gives the following energy levels

where B is rotational
constant in cm^{-1} and J is the angualr
momentum

given E(J)=7 and B= 1.695cm^{-1}

7 = 1.695J(J+1)

by solving the above equation

the angular momentum,J=1.59

the rotational energy

by solving the above equation, the rotational energy = 6.98Joules

where v = rotational quantum number given = 8

w = rataional frequency and rotational energy = 6.98 J

by solving the above equation ,

rotation frequency = 0.8211 Hz

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