关于臭氧半衰期的计算公式?

2024-11-29 03:58:11
推荐回答(3个)
回答1:

先确定是臭氧衰变成氧气。根据一般的半衰期公式有:
公式:
N'=N0*(0.5)^n,M'=M0*(0.5)^n.(n=t/τ)

N'、M'为衰变后剩余原子数和质量。

N0、m0为衰变前原子数和质量。

n为半衰期个数,t所用时间,τ为半衰期。

代入得(用质量近似计算):
最先1小时产生的到T时衰变的是:m1=Q*(0.5)^(T/τ);
第二小时的是:m2=Q*(0.5)^[(T-1)/τ];
…………
最后一小时的是:mT=Q*(0.5)^(1/τ)。

把他们加起来,就是衰变了的质量。
m衰总=m1+m2+……+mT
=Q*{(0.5)^(T/τ)+(0.5)^[(T-1)/τ]+(0.5)^[(T-1)/τ]+……+(0.5)^(1/τ)}
这是一个等比数列,公比a=0.5^(1/τ),然后求和:
m衰总=Q*{[(0.5)^(T/τ)]*[1-(0.5)^(T/τ)]}/[1-(0.5)^?/τ)]
m总=Q*T
T小时后的臭氧质量m=m总-m衰总
=Q*T-Q*{[(0.5)^(T/τ)]*[1-(0.5)^(T/τ)]}/[1-(0.5)^(1/τ)]
最后是用m除以v求得浓度。
OK!
请看清楚运算顺序,我已经好小心的了。
我想了好久的.

回答2:

这是一道无法用初等数学计算的问题,因为每一个时刻都在衰变。

高等数学解法:
设过了x小时,臭氧的质量是y克,我们做微分的假设,即dx时间内无衰变,则:
dy=Qdx-y(1/2)^(dx/t)

然后解这个微分方程就可以了。微分方程的解法我忘记了。

回答3:

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