Question

Please Help!

As a health physicist, you are being consulted about a spill in a radiochemistry lab. The isotope spilled was 500 mu Ci of 131_Ba^75_56, which has a half life of 12 days. What is the mass of 131_Ba^75_56 was spilled? your recommendation is to clear the lab unit the radiation level has fallen below 1.00 mu Ci. How long will the lab have to be closed?

Answer 1

a)

dN/dt = 500 uCi = (500 x 10^-6)*(3.70 x 10^10 1/s) = 1.85 x 10^7 decay/sec.

T1/2 = ln(2) / $\lambda$

$\lambda$ = ln(2) / T1/2

$\lambda$ = ln(2) / 12d*(86400 s/d) = 6.69 x 10^-7 s

dN/dt = $\lambda$ *N

N = (dN/dt)/ $\lambda$

N = (6.69 x 10^7 sec) / (1.85 x 10^-7 decay/sec)

N = 2.77 x 10^13 nuclei

The mass of 131Ba nuclei is

m = 2.77 x 10^13 x (131 x 1.67 x 10^-27 kg/nucleus) = 6 x 10^-12 kg

m = 6 x 10^-9 gm

m = 6 ng.

b)

A = A0e^- $\lambda$ t

1 uCi = (500 uCi)*e^- $\lambda$ t

t = -ln(1/500) / $\lambda$

t = -ln(1/500) / (6.69 x 10^-7 1/sec)

t = 9.29 x 10^-6 sec (1d / 86400 sec)

t = 108 days