Calculating Radioactive Au(A=198) and Hg(A=198) After 5 Days of Bombardment

[shahar weiss]

Here's a ques. I am having problem with:
sample of gold is bombard with 2*10^10 neutrons per sec. it cause the Au(A=197) become radioactive (Au(A=198)) which decay with half life time of 2.969day (through beta decay
1. how many Au(A=198) will be after 5 days of bombardment?
2. how many Hg(A=198) will there be after 5 days?
3. what is the number of radioactive Au(A=198) at equilibrium and what will be the activity of the sample?

im having problem getting the differential equations right here, ill be very happy for any help. thank you so much in advance

 

[Rick88]

Have you tried with

?R.

 

[Redbelly98]

Welcome to physics forums.

Here's a ques. I am having problem with:
sample of gold is bombard with 2*10^10 neutrons per sec. it cause the Au(A=197) become radioactive (Au(A=198)) which decay with half life time of 2.969day (through beta decay
1. how many Au(A=198) will be after 5 days of bombardment?
2. how many Hg(A=198) will there be after 5 days?
3. what is the number of radioactive Au(A=198) at equilibrium and what will be the activity of the sample?

im having problem getting the differential equations right here, ill be very happy for any help. thank you so much in advance

Okay, there are two things to think about here concerning the Au-198:

• At what rate are Au-198 atoms created?
• At what rate are Au-198 atoms destroyed (i.e they decay)?

Those two rates determine what $$\frac{dN}{dt}$$ is for Au-198.

 

[shahar weiss]

Have you tried with

?


R.

wont work here since there are two different half life times, two different activities, two different decay constants.
your formula is good when there is simple decay from some amount of radiactive sample.
here the sample's size changing all the time