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Q12P

Expert-verifiedFound in: Page 1182

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**Under ideal conditions, a visual sensation can occur in the human visual system if the light of wavelength 550nm is absorbed by the eye’s retina at a rate as low as 100 photons per second. What is the corresponding rate at which energy is absorbed by the retina?**

The rate at which energy is absorbed by photon is $3.6\times {10}^{-17}\mathrm{W}.$

**The energy of a photon is given by,**

${E}{=}\frac{hc}{\lambda}$ ….. (1)

**Here, h is Planck’s constant, ${\lambda}$ is the wavelength, and c is the speed of light.**

Consider the given data as below.

The wavelength, $\lambda =550nm.$

Plank’s constant, $\mathrm{h}=6.626\times {10}^{-34}\mathrm{J}.\mathrm{s}.$

The speed of light, $\mathrm{c}=3\times {10}^{8}\mathrm{m}/\mathrm{s}$

Substitute the below values in eq 1.

$\mathrm{c}=3\times {10}^{8}\mathrm{m}/\mathrm{s}\phantom{\rule{0ex}{0ex}}\mathrm{h}=6.626\times {10}^{-34}\mathrm{J}\xb7\mathrm{s}\phantom{\rule{0ex}{0ex}}\mathrm{\lambda}=550\mathrm{nm}$

$E=\frac{\left(6.626\times {10}^{-34}\mathrm{J}\xb7\mathrm{s}\right)\left(3\times {10}^{8}\mathrm{m}/\mathrm{s}\right)}{\left(550\mathrm{nm}\right)\left(\frac{1\mathrm{m}}{{10}^{9}\mathrm{nm}}\right)}\phantom{\rule{0ex}{0ex}}=0.036\times {10}^{-17}\mathrm{J}\phantom{\rule{0ex}{0ex}}=3.6\times {10}^{-19}\mathrm{J}$

Find the energy absorbed by retina as follows.

$\mathrm{energyabsorbedbyretina}=\left(\mathrm{photon}\mathrm{per}\mathrm{second}\right)\left(\mathrm{energy}\mathrm{of}\mathrm{the}\mathrm{photon}\right)\phantom{\rule{0ex}{0ex}}=(100\mathrm{photons}/\mathrm{s})\left(3.6\times {10}^{-19}\mathrm{J}/\mathrm{photons}\right)\phantom{\rule{0ex}{0ex}}=3.6\times {10}^{-17}\mathrm{J}/\mathrm{s}\phantom{\rule{0ex}{0ex}}=3.6\times {10}^{-17}\mathrm{W}$

Hence, the rate at which energy is absorbed by photon is $3.6\times {10}^{-17}\mathrm{W}.$

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