hw_7_solu

hw_7_solu - ME 125NT Intro to Nanotechnology Due: 5/27/2008...

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ME 125NT Intro to Nanotechnology Due: 5/27/2008 1 Solution Set 7 Problem 8.22 in book Solar radiation in the wavelength range of 290-400 nm burns our skin. (a) What range of the electromagnetic spectrum do these wavelengths correspond to? (b) A batch of particles with band gaps ranging from 3.0 to 3.5 eV is prepared for use in sunscreen. What percentage of the harmful wavelengths can this range of particles absorb? ANSWER A) Ultraviolet B) ( )( ) J 10 4.8 s / m 299792458 s / kg m 10 6.626 19 - 2 -34 × × = = E hc λ = 413 nm ( )( ) J 10 6 5 s / m 299792458 s / kg m 10 6.626 19 - 2 -34 × × = = . E hc = 354 nm Since these particles cover wavelengths not only in the right range but also some outside it, we can only include a portion of the wavelengths absorbed in the calculation: (400-354)/(400-290) = 42% Problem 8.31 in book The luminosity of the sun is 3.827×10 26 Watts (1 Watt = Joule/s). This is the approximate power it emits over a range of photon wavelengths, in all directions, out into the solar system. The distance from the earth to the sun is approximately 150,000,000 km (Figure 8.13). The earth’s diameter is 12,756 km. (a) Assuming no photons are absorbed or scattered in the space between the sun and the earth, how much of this power is incident on the earth’s surface? (b) We’ll assume that 40 percent of the sun’s total luminosity is emitted at a wavelength of 550 nm. (This happens to be yellowish light). What is the energy (in Joules) of a single photon with this wavelength? (c) How many photons with this wavelength are incident on the earth every second? (d) What is the momentum carried by a second’s worth of these 550 nm- wavelength, earth-bound photons? (e) The heaviest train ever pulled weighed 99,790,321 kg. (It had 5,648 wheels, measured over 7 km long and traveled across part of Western Australia on June 21, 2001—according to Guinness World Records, 2006). How fast would this train have to travel (in m/s) to have momentum equal to the photons you calculated in part (d)? ANSWER A) Considering the sun as the center of a sphere with radius 150,000,000,000 m, the total sphere surface area is: 4 π (150×10 9 m) 2 = 2.83×10 23 m 2 . Then, treating the earth as a circular area on the larger sphere, like a tiny dot that blocks some of the concentrically
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ME 125NT Intro to Nanotechnology Due: 5/27/2008 2 radiating photons, we determine the area of incidence: π (12,756,000 m) 2 = 5.11×10 14 m 2 .
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hw_7_solu - ME 125NT Intro to Nanotechnology Due: 5/27/2008...

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