Q5DQ Analysis of the photon absorptio... [FREE SOLUTION]

91影视

University Physics with Modern Physics

Hugh D. Young, Roger A. Freedman

Physics

14th edition Edition 路 1596 pages

ISBN: 9780321973610

Chapter 6: Q5DQ (page 1434)

Analysis of the photon absorption spectrum of a diatomic molecule shows that the vibrational energy levels for small values of n are very nearly equally spaced but the levels for large n are not equally spaced. Discuss the reason for this observation. Do you expect the adjacent levels to move closer together or farther apart as n increases? Explain.

Short Answer

Expert verified

The vibrational energy is directly proportional to the energy level, thus, for larger the energy levels, larger will be the vibrational energy. As the vibrational energy decides the energy separation for two consecutive levels, thus for higher energy levels, the energy will be greater. Hence, as the energy level increases, the levels move further apart.

Step by step solution

Significance of absorption spectrum

When electrons absorb energy from their ground state to reach higher energy states, they emit light at frequencies with dark bands. Atoms absorb energy to create this kind of spectrum.

Determine the reason for the given observation.

The vibrational energy levels of a diatomic molecule is calculated using

$E_{n} = I (n + \frac{1}{2}) h w$

Now, the energy separation is then determined by

$鈭� E = h w$

Now, the vibrational energy increases as the energy level increases. The energy separation also increases as the vibrational energy increases. Hence, as the energy level n increases, the adjacent levels move further apart.