# Homework Help: Need help on a half life equation

1. Sep 10, 2009

### fuzzybear

1. The problem statement, all variables and given/known data
Given Y=Ae-t/(lambda) find the half life in terms of A and lambda

2. Relevant equations

Y=Ae-t/(lambda)

3. The attempt at a solution
every time t is a multiple of lambda the relationship then becomes (lambda(n)=A/e^n), i cant figure out how that will relate, i also tried setting the equation to A/2 however that just canceled out the A. Need help!
I figured it out t(1/2)=ln(2)/lambda, however i dont know how to incorporate A into this

Last edited: Sep 10, 2009
2. Sep 10, 2009

### rl.bhat

Expression of radioactive is written as
A = Ao*e^-λt.......(1)
As you have mentioned
t_1/2 = ln(2)/λ.
The equation (1) can be written as
A/Ao = e^-λt. or
Ao/A = e^λt
Take logarithm of both the side and fine the expression for λ. Put it in the t_1/2 equation.

3. Sep 10, 2009

### fuzzybear

rl.bhat if i put the expression into lambda in the t_1/2 equation then i lose the lambda, i need to express it in lambda and A

4. Sep 10, 2009

### rl.bhat

In that case
t_1/2 = ln(A/Ao)/λ