MHB What is the decay constant of tritium?

[tcking3]

"Tritium is the basic fuel of hydrogen bombs and is used to increase the power for fission bombs . . . In a basic atom bomb (or reactor), plutonium atoms are split, or fissioned, to release energy, but the fission can be promoted with a small amount of tritium because it has two extra atom-splitting neutrons. Plutonium is a relatively stable material, and its natural decay is not a major factor in bomb maintenance. Tritium, however, decays at a rate of 5.5percent a year."

What is the half life of tritium?

I think you would need to set up an A(t)= Ae^rt equation but I am having trouble pinpointing what to put in.

 

[MarkFL]

You could state:

$$A(t)=A_0e^{-kt}$$

where $t$ is measured in years.

Now, using the given information, what is $A(1)$?

 

[SuperSonic4]

"Tritium is the basic fuel of hydrogen bombs and is used to increase the power for fission bombs . . . In a basic atom bomb (or reactor), plutonium atoms are split, or fissioned, to release energy, but the fission can be promoted with a small amount of tritium because it has two extra atom-splitting neutrons. Plutonium is a relatively stable material, and its natural decay is not a major factor in bomb maintenance. Tritium, however, decays at a rate of 5.5percent a year."

What is the half life of tritium?

I think you would need to set up an A(t)= Ae^rt equation but I am having trouble pinpointing what to put in.

Generally exponential decay is written as $$A(t) = Ae^{-rt}$$ although all this does is change the sign of $$r$$.To find the decay constant, [math]r[/math] find out what happens after 1 year (ie: when $$t = 1$$)Half-life and the decay constant are linked by the equation $$t_{1/2} = \dfrac{\ln(2)}{r}$$ (you can show this from your original equation)