Chapter 6, Problem 64GQ

### 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

# Exposure to high doses of microwaves can cause tissue damage. Estimate how many photons, with λ = 12 cm, must be absorbed to raise the temperature of your eye by 3.0 °C. Assume the mass of an eye is 11 g and its specific heat capacity is 4.0 J/g · K.

Interpretation Introduction

Interpretation: The number of photons with λ=12cm has to be calculated.

Concept introduction:

• Planck’s equation,

E=where, E=energyh=Planck'sconstantν=frequency

The energy increases as the wavelength of the light decrease. Also the energy increases as the frequency of the light increases.

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

ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

• The specific heat capacity can be calculated as,

Q=mCpΔTwhere,Q=specificheatcapacitym=massCp=specificheatΔT=changeintemperature

Explanation

The number of photons with Î»â€‰=â€‰12â€‰cm is calculated

Given,

â€‚Â Massâ€‰=â€‰11â€‰gRaiseâ€‰inâ€‰temperatureâ€‰=â€‰30â€‰CSpecificâ€‰heatâ€‰=â€‰4.0â€‰J/g.KWavelengthâ€‰=â€‰12â€‰cmâ€‰=0.12â€‰mspeedâ€‰ofâ€‰light,câ€‰=â€‰2.998â€‰Ã—â€‰10â€‰8â€‰m/sPlanck'sâ€‰constant,hâ€‰=â€‰6.626â€‰Ã—â€‰10â€‰-34â€‰J.s

The specific heat capacity is the total energy required to increase the temperature.

â€‚Â Qâ€‰=â€‰mâ€‰Cpâ€‰Î”T=â€‰11â€‰gâ€‰Ã—â€‰â€‰4.0â€‰J/g.Kâ€‰Ã—â€‰30â€‰C=â€‰132â€‰J

Hence, the energy is 132â€‰J

The frequency is,

Â Â Â Â Î½â€‰=â€‰cÎ»Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

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