   Chapter 6, Problem 64GQ

Chapter
Section
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 λ=12cm is calculated

Given,

Mass=11gRaiseintemperature=30CSpecificheat=4.0J/g.KWavelength=12cm=0.12mspeedoflight,c=2.998×108m/sPlanck'sconstant,h=6.626×10-34J.s

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

Q=mCpΔT=11g×4.0J/g.K×30C=132J

Hence, the energy is 132J

The frequency is,

ν=cλ

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