(adsbygoogle = window.adsbygoogle || []).push({}); (a) If galactic cosmic rays produce 75 gm of [itex] ^{14} C [/itex] per year in Earth’s atmosphere, the [tex]^{14} C [/itex] resides in the atmosphere as 14CO2 and the radioactive decay half life of [itex] ^{14} C [/itex] is 5730 years, calculate the total mass of [itex] ^{14} [/itex]CO2 in the atmosphere.

ok the half life equation is quite simple... quantity after time, t is

[tex] q(t) = 2^{-\frac{t}{5760}} [/tex]

would this form something of a differential equation?

[tex] \frac{dq}{dt} = 75g/yr - \frac{2^{-\frac{t}{5760}}}{5760} [/tex]

the equilibrium of this sytem would be when the out rate is equal tothe in rate... from this i can solve for t... which i then sub into the equation for q(t) ?

Is that good?

(b) If the cosmic ray production rate suddenly increased to 150 gm of 14C per year which of the following would be true about the total mass of 14CO2 in the atmosphere 11 years after the increase in the cosmic ray production rate (explain your answer):

(i) The amount of 14CO2 in the atmosphere would have doubled.

(ii) The amount of 14CO2 in the atmosphere would have increased by (11/5730) x 100%

(iii) The amount of 14CO2 in the atmosphere would have increased only very slightly.

i guess i could answer this one if i knew if 1 was a) was done correctly?

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# Half life

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