Half Life Problems

[soccerball3211]

Polonium 218 has a half life of 3.0 minutes. A sample weighing 50.0g is stored on a laboratory shelf. How much of the isotope will remain after 15 minutes had passed.

A block of radium 226 weighs 1.0x10^4 kg. How much of this radioisotope will remain after 6500 years have passed?

A sample of cesium 138 is produced in a lab. The sample weighs 100.0g at the time it is produced. How long will it take before this sample is reduced to only 20g. The half life of cesium 138 is 32.2 minutes.

A sample of oxygen gas contained within a glass tube includes 7.4g of the radioisotope oxygen 15. At what later time will the amount of oxygen 15 be reduced to only 0.5g.

 

[tkhunny]

Polonium 218 has a half life of 3.0 minutes. A sample weighing 50.0g is stored on a laboratory shelf. How much of the isotope will remain after 15 minutes had passed.

t is in minutes
a is a constant

Polonium219(t) = P₀*a^t

a³ = ½

Solve for 'a' however you wish.

a = 0.7937

Check: 0.7937³ = 0.499999005953 -- That's pretty close.

Polonium219(t) = P₀*0.7937^t

Polonium219(t) = (50.0 gm)*0.7937^t

Polonium219(15) = (50.0 gm)*0.7937¹⁵

That's about it, really. Now you show me one.

 

[soccerball3211]

Half Life

For the 2nd one I got: 598.502 kg

For the 3rd one I got: 74.766 minutes

And, for the 4th one I got: 474.97 seconds later

 

[tkhunny]

Where did you get the half-life of radium? I don't see it in the problem statement. One sufficently ingenious to go find standard published values gets extra credit in my book. A little searching shows Radium 226 at 1620 years.

Sorry, I get 619.674 kg -- Actually, with only two significant digits, that's 620 kg.

 

[tkhunny]

Where did you get the half-life of radium? I don't see it in the problem statement. One sufficently ingenious to go find standard published values gets extra credit in my book. A little searching shows Radium 226 at 1620 years.

Sorry, I get 619.674 kg -- Actually, with only two significant digits, that's 620 kg.