How Long Until 24Na Decays from 5μg to 1μg?

[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?

 

[SammyS]

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?

Hello kkid. Welcome to PF !

What's the formula for radioactive decay?

 

[kkid]

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)

 

[SammyS]

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)

Yes, that's correct.

Without rounding until the final answer, I get t_1/5 = 543.331 hours .