Half Life

msjenkins521 · #1 Oct 22, 2009, 11:09 AM

If you have 400g of substance x, x has a half life of 20 seconds, after 1 minute, how much is left?

Unknown008 · Oct 22, 2009, 11:16 AM

The equation for the half life of a substance is:

${N = N_o\, \times\, 2^{-$\frac{t}{t_{\frac12}}$}}$

Where N is your final amount of substance, N_o the initial amount, t your time, t_0.5 your half life.

ebaines · Oct 22, 2009, 11:20 AM

This is more of a math or physics question than astronomy, but I'll take a shot at it:

If the half life is 20 seconds, that means that in each 20-second interval half of what you started with at the beginnng ofthat inerval is gone. So you start with 400g at T= 0 seconds, and at T=20 seconds you would have halfof 400g, or 200g left. 20 seconds later, at T=40 you would have half of the 200g, or 100g. Can you take it from here - how much material is left at T=60 seconds?

ebaines · Oct 22, 2009, 11:21 AM

Quote:

Originally Posted by Unknown008

The equation for the half life of a substance is:

${N = N_o\, \times\, 2^{$\frac{t}{t_{\frac12}}$}}$

Where N is your final amount of substance, N_o the initial amount, t your time, t_0.5 your half life.

I think you need to divide $N_o$ by $2^{$\frac{t}{t_{\frac12}}$}$ - not multiply.

Unknown008 · Oct 22, 2009, 11:23 AM

Sorry, I realised my mistake a little late, I fixed it before you posted

msjenkins521 · Oct 22, 2009, 11:28 AM

Quote:

Originally Posted by ebaines

This is more of a math or physics question than astronomy, but I'll take a shot at it:

If the half life is 20 seconds, that means that in each 20-second interval half of what you started with at the beginnng ofthat inerval is gone. So you start with 400g at T= 0 seconds, and at T=20 seconds you would have halfof 400g, or 200g left. 20 seconds later, at T=40 you would have half of the 200g, or 100g. Can you take it from here - how much material is left at T=60 seconds?

Thank you very much