What is the specific activity of the air inside the sealed warehouse?

[xamy]

Can anyone please guide me how to find solution of this problem

A 0.2-g sample of 85Kr gas, which decays into stable 85Rb, is accidentally broken and escapes inside a sealed warehouse measuring 40×30×20 m. What is the specific activity of the air inside?

 

[Astronuc]

Specific activity is a function of mass, so the mass shouldn't change. The activity per unit volume will decrease if the gas disperses in the air/volume.

Also, Kr is a heavy gas and will tend to settle, although some would mix in the air.

The activity is given by the product of the decay constant and the number of atoms of a given species. The specific activity is simply the activity divided by the mass.

 

[xamy]

Thankyou for your reply

I have found the specific activity as a function of mass. But how to find the specific activity according to the volume mentioned in the question?
SA = 4.17×1023/ MT

SA=4.17×1023/ (85)(10.72x365x24x3600)

SA=14.5116TB q/g

1g=14.5116TBq

0.2g=2.902322927TBq

 

[xamy]

Using the theory that you have explained I have found the answer. Thank you so much

 

[Astronuc]

Caveat - if the question is asking for specific activity in the air, as opposed to specific activity if the Kr gas, then one would have to consider the dilution of the Kr gas in the air, and consider the mass of the air.

Activity could be given in terms of activity per volume of atmosphere, or mass of air, so one would consider the activity from the mass of the Kr-85, but then divide by the mass or volume of the combined air+Kr gas.

So the basis of the activity is important.

Is there any guidance in one's textbook as to the basis or units of the specific activity?

FYI - http://hpschapters.org/northcarolina/NSDS/krypton.pdf