Question

Consider a gas of diatomic molecules (moment of inertia I) at an absolute temperature T. If Eg is a ground-state energy and Eex is the energy of an excited state, then the Maxwell-Boltzmann distribution predicts that the ratio of the numbers of molecules in the two states is nexng=e−(Eex−Eg)/kT. The ratio of the number of molecules in the lth rotational energy level to the number of molecules in the ground-state (l=0) rotational level is nln0=(2l+1)e−l(l+1)ℏ2/2IkT. The moment of inertia of the CO molecule is 1.449×10−46kg⋅m2. (Hint: For each value of l, how many states are there with different values of ml?)

Part A)

Determine the ratio nl/n0 for a gas of CO molecules at 296 K for l= 1.

Express your answer using three significant figures.

Part B)

Determine the ratio nl/n0 for a gas of CO molecules at 296 K for l= 3.

Express your answer using three significant figures.

Part C)

Determine the ratio nl/n0 for a gas of CO molecules at 296 K for l= 11.

Express your answer using three significant figures.

Part D)

Determine the ratio nl/n0 for a gas of CO molecules at 296 K for l= 20.

Express your answer using three significant figures.

Part E)

Determine the ratio nl/n0 for a gas of CO molecules at 296 K for l= 46.

Express your answer using three significant figures.

Part F)

▼ Part F Your results show that as l is increased, the ratio ni no first increases and then decreases. Explain why Drag the terms on the left to the appropriate blanks on the right to complete the sentences. Reset Help There is a competing effect between the term and the decaying exponential. The term dominates for small ,while the exponential term dominates for large large 2l 2n small l Submit Request Answer

Answer 1

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31 kg m 스3:e B) N3 (2x319 e X11.4リ, e No 132 h 23 x e 20 +1 3-95 -70-73
this is because the rotational energy levels are more closely spaced at lower values of l. But as the value of l increase the space between two consecutive energy levels also increase. Moreover at the given temperature of 296K the particles have enough energy to occupy higher levels of l. But not so much that they can occupy very high values of l like l=46 or l=20.