Question

The Transportation Security Administration stopped a suspicious passenger and found some radioactive material on the individual. A 1000 gram sample is found to have an activity of 2.3×10^12 becquerels. The sample is most likely:
a) Sr-90 b) Pu-239 c) U-235 d) Cs-137

Answer 1

Activity is the amount of decays.
\[\lambda=\frac{1}{t_{\frac{1}{2}}}\]\[A=2.3*10^{12}=\lambda N=\lambda \frac{1000}{A_{r}}*6.022*10^{23}\]

The substance is thus whatever that satisfy the relation:
\[t_{\frac{1}{2}}*A_{r}=2.62*10^{14}\]

The closest fit would be plutonium.

Answer 2

Ah thanks i've got it now, (you forgot the ln2 )

Answer 3

For general info and for anyone else reading this post, you cannot in reality solve this problem with the information provided. Isotopes are identified by their decay radiation which is unique to an isotope.

The problem assumes that the material is pure. which is almost impossible to have from a practical point of view. It assumes that it has determined the mode of decay in that case it already knows the isotope. You can only determine the activity from counting the radiation if you know what radiation results from one decay.

It also assume that it is a single isotope and not a mixture which would be a ridiculous assumption also.

Answer 4

Yeah i agree that the question isn't very good, and certainly isn't realistic

Answer 5

the lecturers 'solution'

Answer 6

my solution

Answer 7

that weird 'characteristic' number has some odd units

Answer 8

My method only worked because I only had four options,
and the lecturers method only worked because the knew the answer

Answer 9

You could narrow it down by looking a the gross characteristics of the radiation. In this case if for some reason you believe that it is one of the four isotopes given. You would know that Sr-90 is a strong Beta emitter, Cs-137 is a high energy gamma emitter. PU239 and U235 are both alpha emitters but to confuse the situation U235 is a decay product of PU239 so both are present if PU239 is present.

Answer 10

i think in a real situation it might be easier to find the atomic mass by finding the measuring the volume (via submerging the mass in water and seeing the displaced volume )

Answer 11

Thank you both @Festinger & @gleem .

Answer 12

Regarding the submerging of a body to find its mass. Way to insensitive beside you have to know it is a pure substance.