Question

A hospital needs 0.100 gg of 133 54Xe 54133Xe for a lung-imaging test. If it takes 10 daysdays to receive the shipment, what is the minimal amount mXemXem_Xe of xenon that the hospital should order? Express your answer numerically in grams

Answer 1

The correct answer will be "0.400 gm".

Explanation:

The give values are:

Needs of hospital, N = 0.100 gm

Time, t = 10 days

Minimum amount of Xenon, N₀ = ?

As we know,

⇒
`N(t)=N_(0) \ e^(-\lambda t)`

∴ Decay constant, λ =
`(ln2)/(t_(1/2))`

λ =
`(ln2)/(5)`

On putting values, we get

⇒
`0.100=N_(0) \ e^{-(ln2)/(5)}* 10`

⇒
`0.1=N_(0) \ e^(-2ln2) = N_(0) \ e^(-ln4)`

⇒
`0.1=N_(0) \ e^{ln(1)/(4)}`

⇒
`0.1=(N_(0))/(4)`

⇒
`N_(0)=0.1* 4`

⇒
`MX_(e)=0.400 \ gm`