First slide

Average energy density of electromagnetic wave

Question

Estimate how many photons of yellow light ( $λ$ = 575 nm) must be absorbed by 1.0 cm³ of human skin to raise the skin temperature by 1.0 °C. Assume that the photon energy is absorbed by 1.0 cm³of tissue. As rough estimates of the tissue's density and specific heat, use the values for water.

Moderate

A

1.3 x 10¹⁹
B

1.1 x 10¹⁹
C

1.4 x 10¹⁹
D

1.2 x 10¹⁹

Solution

$\begin{array}{rcl} ms ∆ T & = & E; \\ (Vd) s ∆ T & = & n \frac{hc}{λ} \\ n & = & \frac{VdsΔTλ}{hc} \\ = & \frac{10^{- 6} \times 10^{3} \times 4200 \times 1 \times 575 \times 10^{- 9}}{6.6 \times 10^{- 34} \times 3 \times 10^{8}} \\ = & 1.2 \times 10^{19} \end{array}$

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