A hospital receives a shipment of a radiopharmaceutical containing

PHYSICS · Multi-part · A Level · Physics · Nuclear physics · Nuclear physics

Problem

^{131}\text{I}

, whose half-life is

8.04\,\text{days}

. The initial activity of the shipment is

50.0\,\text{MBq}

. For patient-safety regulations, the activity must fall below

1.00\,\text{MBq}

before the remaining material can be discarded as non-radioactive waste. (1) Calculate the numerical value of the decay constant

\lambda

for

^{131}\text{I}

, including proper units. (2) Determine the elapsed time required for the activity to decrease from

50.0\,\text{MBq}

to the

1.00\,\text{MBq}

threshold. (3) Express your result from part (b) in the form “

x

days

y

hours,” where

0\le y<24

. Briefly interpret what this time interval means in the context of the hospital’s disposal schedule.