Question

A hospital needs 0.100 g of 133 54Xe for a lung-imaging test. If it takes 10 days to receive the shipment, what is the minimal amount mXe of xenon that the hospital should order?

Answer 1

Answer:

the hospital needs to order for a  minimum amount of 0.4 g of $\left \ {{133} \atop {54} \right. Xe$

Explanation:

Given that:

A hospital needs 0.100 g of $\left \ {{133} \atop {54} \right. Xe$

and it takes 10 days for the shipment to arrive:

the half life $t_{1/2}$ = 5 days

So, since the half life = 5 days ;

decay constant $\lambda = \frac{In_2}{t_{1/2}}$

where:

$N_o= ??? \\ \\ N = 0.1 00 \\ \\ t = 10 days \\ \\ N(t)= N_oe^{-\lambda t}\\ \\0.1 = N_oe^{\frac{-In_2}{5} *10} \\ \\0.1 = N_oe^{ - In \ 4} \\ \\ 0.1 = N_oe^{ In \frac{1}{ 4}} \\ \\ 0.1 = \frac{N_o}{4} \\ \\ N_o = 0.1*4 \\ \\ N_o = 0.4 \ g$

Therefore in order to get 0.100 g  of $\left \ {{133} \atop {54} \right. Xe$, the hospital needs to order for a  minimum amount of 0.4 g of