Question

The half-life of radioactive 55Cr is 1.8 hours. The delivery of a sample of this isotope from the reactor to your laboratory requires about 10.8 hours. What is the minimum amount of such material that should be shipped in order that you receive 1.0 milligram 55 Cr?

Answer 1

Answer:

The minimum amount of such material that should be shipped is 63.9 mg≅ 64 mg.

Explanation:

Given Data:

Half life=1.8 hours

Formula:

Half life=0.693/k

Where:

k is rate constant

k=0.693/1.8

k=0.385 hr^-1

Formula to find initial concentration:

$ln\frac{A}{A_o}=-kt$

Where:

A is final concentration

A_o is initial concentration

t is time

Taking exponential on both sides:

$\frac{A}{A_o}=e^{-kt}\\ A_o=\frac{A}{e^{-kt}}\\ A_o=63.9 mg$

The minimum amount of such material that should be shipped is 63.9 mg≅ 64 mg.