   Chapter 6, Problem 20PS

Chapter
Section
Textbook Problem

If energy is absorbed by a hydrogen atom in its ground state, the atom is excited to a higher energy state. For example, the excitation of an electron from n = 1 to n = 3 requires radiation with a wavelength of 102.6 nm. Which of the following transitions would require radiation of longer wave- length than this? (a) n = 2 to n = 4 (b) n = 1 to n = 4 (c) n = 1 to n = 5 (d) n = 3 to n = 5

Interpretation Introduction

Interpretation:

The half transition that needed for radiation with longer wavelength than n=1 to the n=3 level is to be determined from the given option.

Concept introduction:

• Electronic transitions that take place in excited H atom is,
1. 1. Lyman series: electronic transitions take place to the n=1 level and it is in ultraviolet region.
1. 2. Balmer series: electronic transitions take place from n>2 to the n=2 level and it is in visible region.
2. 3. Ritz-Paschen series: electronic transitions take place from n>3 to the n=3 level and it is in infrared region.
3. 4. Brackett series: electronic transitions take place from n>4 to the n=4 level.
4. 5. Pfund series: electronic transitions take place from n>5 to the n=5 level

As the energy gap between two transition states increases the frequency of the radiation emitted also increases (E=hν)

Explanation

Reason for correct option:

The energy is low when the differences in energy levels are small which implies that it has higher wavelength.

The wavelength of radiation emitted increases as the differences in energy levels are decreases.

Therefore, in a transition, the radiations with longer wavelength than n=1 to the n=3 level are emitted from n=2 to the n=4 level.

Hence the correct option for the transition that needed for radiation with longer wavelength than n=1 to the n=3 level is option a.

Reasons for incorrect options:

Write all the transition that needed for radiation with longer wavelength than n=1 to the n=3 level given in the options except option a

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