What frac tion of the beam is absorbed in passing through a layer containing 1

What frac tion of the beam is absorbed in passing

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1. What frac-tion of the beam is absorbed in passing through a layer containing 1 kgm2of the gas?What mass of gas would the layer have to contain onorder to absorb half the incident radiation?
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per unit mass(and consequentlythe heating rate) is strongest, not at the level of unit optical depth butnear the top of the atmosphere, where the incident radiation is virtuallyundepleted. 65
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4.46Consider a hypothetical planetary atmosphere comprised entirely of thegas in Exercise 4.43. The atmospheric pressure at the surface of the planetis 1000 hPa, the lapse-rate is isothermal, the scale height is 10 km and thegravitational acceleration is 10 m s2.Estimate the height and pressureof the level of unit normal optical depth.At the level of unit normal optical depthτλ=kλZzρdz= 1Hence,kλgZzρgdz=kλpg= 1It follows thatp=gkλ=100.01= 103PaFrom the hypsometric equationz=Hlnμp0p=10 ln 100=46km4.47(a) What percentage of the incident monochromatic intensity with wave-lengthλand zero zenith angle is absorbed in passing through the layerof the atmosphere extending from an optical depthτλ=0.2 toτλ=4.0?(b) What percentage of the outgoing monochromatic intensity to spacewith wavelengthλand zero zenith angle is emitted from the layer of theatmosphere extending from an optical depthτλ=0.2 toτλ=4.0? (c)In an isothermal atmosphere, through how many scale heights would thelayer in (a) and (b) extend?
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