Solving Radioactive Decay: Homework Equations and Attempt at Solution

[elemis]

Homework Statement

Homework Equations

N=N₀e^-λt

The Attempt at a Solution

I can do all of part (a) but I'm stuck on part (b).

I don't even know where to begin. I just have no idea what to make of this question.

Could someone prod me in the right direction ?

 

[gneill]

What's the expression for the activity of a sample over time, given its half-life and initial activity value?

 

[elemis]

What's the expression for the activity of a sample over time, given its half-life and initial activity value?

I've written down that expression in the original post.

 

[gneill]

I've written down that expression in the original post.

Not quite, you've written down the amount of material remaining as a function of time. The rate of decay is measured in Becquerels (Bq) and represents the instantaneous number of decays per second. It has a similar form to the equation you wrote...

 

[elemis]

Not quite, you've written down the amount of material remaining as a function of time. The rate of decay is measured in Becquerels (Bq) and represents the instantaneous number of decays per second. It has a similar form to the equation you wrote...

Its basically the same equation except N is subbed for A and N0 for A0

 

[gneill]

Its basically the same equation except N is subbed for A and N0 for A0

Correct. And you're given a value for A_o are you not?

What would constitute a "current" value for A that would represent a maximum deviation of 10% from A_o? Keep in mind that A_o has an initial uncertainty of 2%.

 

[elemis]

Correct. And you're given a value for A_o are you not?

What would constitute a "current" value for A that would represent a maximum deviation of 10% from A_o? Keep in mind that A_o has an initial uncertainty of 2%.

So A₀ = 3.5*10⁵

3.78*10⁵ ? A 2% uncertainty is built into A₀ so an 8% error must originate from the A ?

So 0.08*3.5*10^5 + 3.5*10^5 = above answer ?

 

[gneill]

You're thinking along the right lines... but keep in mind that the Activity must decrease over time. So the new value of A should be smaller than A_o.