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kkurt
2 days ago
3

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 a

mount mXe of xenon that the hospital should order?
Physics
1 answer:
kicyunya [2.9K]2 days ago
7 0

Response:

the hospital should request a minimum quantity of 0.4 g of \left \ {{133} \atop {54} \right. Xe

Clarification:

Considering that:

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

and it takes 10 days for delivery:

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

Thus, since the half-life is 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

Thus to obtain 0.100 g of \left \ {{133} \atop {54} \right. Xe, a minimum order of 0.4 g of

is necessary.
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