The polonium isotope 210Po, an alpha emitter, has a half-life of 138

[MozAngeles]

Homework Statement

The polonium isotope 210Po, an alpha emitter, has a half-life of 138.38 days. You happen to have a 1.5 g cube of 210Po, so you decide to use it to boil water for tea. You fill a well-insulated container with 120 mL of water at 18° C and drop in the cube of polonium.
(a) How long will it take to bring the water to a boil?
(b) Explain whether or not the water have been altered in any way by this method of boiling.

Homework Equations

N=N₀e^-λt
E=mc²
E=mΔTC
where c is heat capacity of water 4.18 j/gC°

The Attempt at a Solution

So far I have found the energy fro the water to change from temperature which is 41131.2 joules. Then I feel i would have to find the amount of time it takes polonium to reach that amount of energy but i don't know how i would do that.

 

[Delphi51]

From the information given, you can figure out how many Polonium atoms you have and how many will decay in a any given time. You also need to know how much energy is released with each decay and that information isn't given. Perhaps you could look it up somewhere.

 

[ehild]

See this article: http://en.wikipedia.org/wiki/Isotopes_of_polonium

ehild

 

[Delphi51]

Amazing how much power that stuff releases! Too bad it isn't practical to power cars with it.

 

[ehild]

Well, it is not used to power cars, but at least "²¹⁰Po heat source was also used in each of the Lunokhod rovers deployed on the surface of the Moon, to keep their internal components warm during the lunar nights."

ehild

 

[Delphi51]

Fascinating! I forgot all about Lunokhod and never heard of its owner before - interesting character. I, too, sold my first Apple II program in ziplok bags at a computer store but unfortunately it didn't interest any company.

 

[ehild]

They still sit on the Moon.
http://www.nasa.gov/mission_pages/LRO/multimedia/lroimages/lroc-20100318.html

ehild

 

[ridebz07]

i'm stuck on the same problem! Anyone figure out yet?? Thanks soo much!

 

[ehild]

We can not help without seeing what you tried so far.

ehild

 

[daveb]

You have that the decay energy of the polonoium is a little over 5 MeV, so you can convert that to joules per decay, and calculate how long the cube of polnum takes to release that much energy (you'll want to convert the mass of the cube to activity first).

 

[Delphi51]

That is the way to do it. You can check your answer for the energy released per second if you carefully read the article linked in post #3.