Chapter 6: Q40P (page 1436)

For the CO molecule at T= 300 K, for what value of is this ratio a maximum? (The moment of inertia of the CO molecule is given in Example 42.2.)

Short Answer

Expert verified

The value of at which this ratio is maximum is 7

Step by step solution

The ratio of the number of molecules in the Ith rotational energy level to the number of molecules in the ground state rational energy

The ratio of the number of molecules in the $l_{th}$ rotational energy level to the number of molecules in the ground state rational energy is given by

$\frac{n_{1}}{n_{0}} = (2 ∣ + 1) e^{- [(1 + 1) \frac{h^{2}}{4 π^{2}}] / 2 ∣ k T}$

The value of at which above ratio is maximum is given by

$I = \frac{2 π \sqrt{I k T}}{h} - \frac{1}{2}$

The calculation of for which this ratio is maximum for the CO molecule at T=300 k

Given:

Moment of inertia the CO molecule is $I = 1.449 \times 10^{- 46} k g . m^{2}$ from example 42.2

Using

$I = \frac{2 π \sqrt{I k T}}{h} - \frac{1}{2}$

Now put the values of constants in above equation

$I = \frac{2 \times 3.14 \times \sqrt{1.449 \times 10^{- 46} kg \cdot m^{2} \times 1.38 \times 10^{- 23} J / K \times 300 K}}{6.63 \times 10^{- 34} J} - \frac{1}{2} I = 6.8445 I = 7 (A p p r o x i m a t e l y)$

Thus, the value of I at which this ratio is maximum is 7.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For the CO molecule at T= 300 K, for what value of is this ratio a maximum? (The moment of inertia of the CO molecule is given in Example 42.2.)

Short Answer

Step by step solution

The ratio of the number of molecules in the Ith rotational energy level to the number of molecules in the ground state rational energy

The calculation of for which this ratio is maximum for the CO molecule at T=300 k

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Modern Physics

Measurements

Electricity

Waves Physics

Fluids

Famous Physicists

Study anywhere. Anytime. Across all devices.