91影视

Nuclear reaction: A nuclear reaction occurs when a lighter nucleus fuses together to form new stable nuclei, or when a heavier nucleus splits into stable daughter nuclei, releasing a large amount of energy.

Considering the given information:

Mass of human = 65 Kg

Energy released in each disintegration =0.156MeV

Amount of ¹⁴C receiving in each yr=10^-8g

Half-life time, t_1/2 of ¹⁴C=5730 yr

The half-life equation will be used to determine the value of k.

$t_{1/2}=\frac{\ln 2}{k}$

Afterthat,rearrangetheequation.

$$\begin{gathered} k=\frac{\ln 2}{t_{1/2}} \\ =\frac{\ln 2}{5730yr} \\ k=1.209脳{10}^{-4}鈥�y{r}^{-1} \end{gathered}$$

Number of moles of ¹⁴C present in${10}^{-8}鈥�g鈥�=\frac{{10}^{-8}g}{14鈥�g/mol}=\frac{{10}^{-8}}{14}鈥�mol$

$$\begin{gathered} \text{狈辞鈥妎蹿鈥奱迟辞尘蝉鈥奿苍鈥�}\frac{{10}^{-8}}{14}鈥�\text{尘辞濒别蝉鈥�}=鈥�6.023脳{10}^{23}脳\frac{{10}^{-8}}{14} \\ =鈥�4.3014脳{10}^{14}鈥�{}^{14}C鈥�鈥�\text{atoms} \end{gathered}$$

Let us calculate the activity.

role="math" localid="1663626119190" $$\begin{gathered} A=kN \\ A=\left.\left(1.209\right.x{10}^{-4}y{r}^{-}\right)\left(4.3014x{10}^{14}\right.atom\left.s^{14}C\right)\left(1\frac{di\sin t.}{atom}\right) \\ A=5.2033x{10}^{10}\frac{di\sin t.}{atom} \end{gathered}$$

We can then calculate the dose value using conversion.

$\frac{5.2033x{10}^{10}\frac{di\sin t.}{year}}{65kg}\left(1year\right)\left(\frac{0.156MeV}{di\sin t.}\right)\left(\frac{1.602x{10}^{-13}}{1MeV}\right)\left(\frac{1rad}{0.01\frac{J}{kg}}\right)=2.001脳{10}^{-3}rad$

Therefore, The required number of Rads (Dose) received by 65 kg human each year is $2脳{10}^{-3}rad$.