Chapter 6, Problem 63GQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Cobalt-60 is a radioactive isotope used in medicine for the treatment of certain cancers. It produces β particles and γ rays, the latter having energies of 1.173 and 1.332 MeV. (1 MeV = 106 electron-volts and 1 eV = 1.6022 × 10−19 J.) What are the wave-length and frequency of a γ-ray photon with an energy of 1.173 MeV?

Interpretation Introduction

Interpretation: The frequency and wavelength of γ-ray photon with an energy of 1.173MeV have to be calculated.

Concept introduction:

• Planck’s equation,

E==hcλwhere, ν=frequencyλ=wavelengthh=Planck'sconstantc=speedoflight

The energy increases as the wavelength of the light decreases.

• The frequency of the light is inversely proportional to its wavelength.

ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

Explanation

The frequency and wavelength of Î³-ray photon with energy of 1.173â€‰MeV is calculated.

Given,

Â Â speedâ€‰ofâ€‰light,câ€‰=â€‰2.998â€‰Ã—â€‰10â€‰8â€‰m/sPlanck'sâ€‰constant,hâ€‰=â€‰6.626â€‰Ã—â€‰10â€‰-34â€‰J.s

Â Â TheÂ energyÂ ofÂ theÂ Î³âˆ’rayâ€‰=1.173â€‰eVâ€‰=â€‰1.173â€‰Ã—â€‰106â€‰Ã—â€‰1.6022â€‰Ã—â€‰10âˆ’19Jâ€‰=â€‰1.879â€‰Ã—â€‰10âˆ’13Jâ€‰

• The frequency of Î³-ray photon with an energy of 1.173â€‰MeV_ is calculated,

â€‚Â Ephotonâ€‰=â€‰hÎ½

Therefore,

Â Â Â Â Î½â€‰=â€‰Ephotonh=â€‰1.879â€‰Ã—â€‰10âˆ’13Jâ€‰â€‰6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J

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