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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 = 10 6 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?

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Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

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Chapter
Section
BuyFindarrow_forward

Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 6, Problem 63GQ
Textbook Problem
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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 of Solution

The frequency and wavelength of γ-ray photon with energy of 1.173MeV is calculated.

Given,

  speedoflight,c=2.998×108m/sPlanck'sconstant,h=6.626×10-34J.s

  The energy of the γray=1.173eV=1.173×106×1.6022×1019J=1.879×1013J

  • The frequency of γ-ray photon with an energy of 1.173MeV_ is calculated,

  Ephoton=

Therefore,

    ν=Ephotonh=1.879×1013J6.626×1034J

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Chemistry & Chemical Reactivity
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