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Physics / An Introduction to Thermal Physics 1 / Chapter A / Problem 22P

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

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In Section 6.2 I used the symbol as an abbreviation for

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QUESTION:

Problem 22P

In Section 6.2 I used the symbol $\varepsilon{}$ as an abbreviation for the constant ${h}^{2}/2l$ . This constant is ordinarily measured by microwave spectroscopy: bombarding' the molecule with microwaves and looking at what frequencies are absorbed.

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QUESTION:

Problem 22P

In Section 6.2 I used the symbol $\varepsilon{}$ as an abbreviation for the constant ${h}^{2}/2l$ . This constant is ordinarily measured by microwave spectroscopy: bombarding' the molecule with microwaves and looking at what frequencies are absorbed.

ANSWER:

Solution

Step 1

To calculate the microwave frequency of the radiation when transition takes place from j=0 level to j=1 for a CO molecule.

The energy required to excite the CO molecule form j=0 level to j=1 level is

$\Delta{}E=hf$

Where h is plank’s constant and f is the frequency.

The energy required to excite the CO molecule from j=0 level to j=1 level is equal to difference between energies of j=1 and j=0 states.

$\Delta{}E={E}_{1}-{E}_{0}$

Here E1 is the energy of the CO molecule for j=1 state and E0 is the energy of the CO molecule for j=0 level.

Substitue ${E}_{1}-{E}_{0}$ for $\Delta{}E$ in the equation

$\Delta{}E=hf$

And solve for f

${E}_{1}-{E}_{0}=hf$

$f={E}_{1}-{E}_{0}/h$

$=1-0/6.6261\times{}1{0}^{-34}$

$=$ 1.5091 $\times{}1{0}^{-34}$

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