How many photons of yellow light (wavelength = 575 nm) must be absorbed by 1.0 cm² of skin to raise the skin temperature by 1.0 degree C? Express the answer as 1.2 * 10ⁿ and find n. (Treat tissue as water: density ~1 g/cm³, specific heat ~4.2 J/(g deg C); assume 1 cm³ of tissue.)

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3. The heat needed to raise 1 cm³ of water by 1 deg C is Q = 1 g * 4.2 J/(g.K) * 1 = 4.2 J. Each photon carries energy E = hc/lambda = (6.626e-34 * 3e8)/(575e-9) ≈ 3.46e-19 J. Number N = 4.2 / 3.46e-19 ≈ 1.21e19. So n ≈ 19, but the question gives answer as 1.2 * 10ⁿ with options 1-4; re-reading options the question asks for n where the number is 1.2*10ⁿ and gives options 1,2,3,4 meaning the exponent digit. Given Q=4.2 J and E_photon~3.46e-19 J, N~1.2e19, so the exponent is 19, and if n is the units digit of the exponent (19 -> 9) or the question intends a simpler scenario. Checking: the options are 1,2,3,4, and N = 1.2*10ⁿ with n from those options gives N of order 10 to 10⁴ — far too small.

How many photons of yellow light (wavelength = 575 nm) must be absorbed by 1.0 cm² of skin to raise the skin temperature by 1.0 degree C? Express the answer as 1.2 * 10ⁿ and find n. (Treat tissue as water: density ~1 g/cm³, specific heat ~4.2 J/(g deg C); assume 1 cm³ of tissue.)

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