# How do I calculate the time taken for an element to decay from one mass to another?

1. Oct 31, 2012

### kkid

TA sample of 24Na has a half-life of 234 hours, How much time elapses before a 5μg sample contains 1μg of undecayed atoms?

I have calculate the decay constant (8.23x10-7)

What do I do now?

2. Oct 31, 2012

### SammyS

Staff Emeritus
Re: How do I calculate the time taken for an element to decay from one mass to anothe

Hello kkid. Welcome to PF !

What's the formula for radioactive decay?

3. Oct 31, 2012

### kkid

Re: How do I calculate the time taken for an element to decay from one mass to anothe

I eventually did this by altering this equation:

N = N0e-λt

if one divides by N0 then the left hand side is just a faction of the start and end amounts (whether this is in terms of amount of atoms or in terms of mass it will be the same.

In this case the left hand side of the equation (the fraction) will be 1/5 as 1 is 1/5 of 5.

This gives me 1/5 = e-λt

taking ln of both sides to eliminate e gives:

ln(1/5) = -λt

t = ln(1/5)/-λ

I substitute the value of decay constant (λ) to get my overall answer of 543.241 hours

Is this correct?
(It took me about 3 hours to get this)

4. Oct 31, 2012

### SammyS

Staff Emeritus
Re: How do I calculate the time taken for an element to decay from one mass to anothe

Yes, that's correct.

Without rounding until the final answer, I get t1/5 = 543.331 hours .