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Chapter 3, Problem 3.1VC

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CHEMISTRY: ATOMS FIRST VOL 1 W/CON...

14th Edition
Burdge
ISBN: 9781259327933

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Chapter
Section
FindFindarrow_forward

CHEMISTRY: ATOMS FIRST VOL 1 W/CON...

14th Edition
Burdge
ISBN: 9781259327933
Interpretation Introduction

Interpretation:

The best explanation for the four lines in the emission spectrum of hydrogen should be explained using the concept of Bohr’s theory from the given statements.

Concept Introduction:

The emission of radiation given by an energized hydrogen atom to the electron falling from a higher-energy orbit to a lower orbit give a quantum of energy in the form of light.  Based on electrostatic interaction and law of motion, Bohr derived the following equation.

En = 2.18 × 1018 J (1n2)

where n gets an integer values such as = 1, 2, 3 and so on.  This is the energy of electron in nth orbital.

The electrons are excited thermally when the light is used by an object.  As a result, an emission spectrum comes.  Line spectra consist of light only at specific, discrete wavelengths.  In emission, the electron returns to a lower energy state from nf (the i and f subscripts denote the initial and final energy states).  In most cases, the lower energy state corresponds to the ground state but it may be any energy state which is lower than the initial excited state.  The difference in the energies between the initial and final states is

ΔE = Ef  Ei

This transition results in the photon’s emission with frequency v and energy hv.  The following equation is resulted.

ΔE = hν = 2.18 × 1018 J (1nf21ni2)

When ni > nf, a photon is emitted.  The term in parentheses is positive, making ΔE negative.  As a result, energy is lost to the surroundings.  When ni < nf, a photon is absorbed.  The term in parentheses is negative, so ΔE is positive.  As a result, energy is absorbed from the surroundings.

Bohr’s theory of the hydrogen atom tells an atom as a small, positively charged nucleus with electrons which travels around the nucleus in circular orbits.  The appearance of an emission spectrum is explained because the “orbits” available for the electrons to occupy in their excited states are quantized.  The resulting transition emits a specific wavelength of light because the energy of the “orbit” is quantized.

images

Figure 1

The emission spectrum of hydrogen shows a wide range of wavelengths from the infrared to the ultraviolet region.  The given table lists the series of transitions in the hydrogen spectrum, each with a different value of nf.  The series are named after their discoverers (Lyman, Balmer, Paschen and Brackett).  The Balmer series was the first to be studied because some of its lines occur in the visible region.

images

Figure 2

The given figure shows transitions associated with spectral lines in each of the emission series.  Each horizontal line represents one of the allowed energy levels for the electron in a hydrogen atom.  The energy levels are labeled with their n values.

images

Figure 3

Correct answer:

The best explanation for the four lines in the emission spectrum of hydrogen is the option (b).

Reason for correct option

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