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

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

Step-by-step 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 = (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^{(-In_2)/(5) *10} \\ \\0.1 = N_oe^( - In \ 4) \\ \\ 0.1 = N_oe^{ In (1)/( 4)} \\ \\ 0.1 = (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