Calculating Decay Constant and Amount of Thorium Plated

[P1nkButt3rflys]

Homework Statement

A small quantity of the thorium isotope Th(A=228, Z=90) (half-life 1.913 y) is prepared and electroplated onto a thick sheet of copper and overcoated with a thin film of gas-tight polymer. The plating and coating are both thin enough so that none of the alpha particles resulting from the decay are absorbed, and all that exit on the film side of the copper sheet are counted. Immediately after preparation, the counter registers 7340 alpha particles per second.

A)What is the decay constant of Th(A=228, Z=90)?

B)How much thorium has been electroplated onto the copper?

Homework Equations

At=Ao*e^[-λ*t]
λ=0.693/T

The Attempt at a Solution

A)
T=1.913y

λ=(0.693/1.913)
λ= 0.181 y^-1

This is incorrect.
Any guidance or hints would be appreciated!

 

[Simon Bridge]

Cannot see your reasoning.
i.e. what proportion of the alphas emitted are counted?

 

[SteamKing]

You must also be using the correct units. The half-life of Th-228 is measured in years and you have an alpha count in particles per second.

 

[P1nkButt3rflys]

I got the first part A)
T=1.913y = 6.037e7 sec

λ=(0.693/6.037e7)
λ=1.15e-8 s^-1

but I have no idea where to start with part b. Any suggestions?

 

[Simon Bridge]

How is the decay rate related to the amount of substance present?

 

[P1nkButt3rflys]

I'm not sure. I feel like I'm missing a formula

 

[Simon Bridge]

You listed two formulas in post #1 and used only one of them.

 

[P1nkButt3rflys]

I was thinking:
At=Ao*e^[-λ*t]
Ao=7340 particles/sec
λ=1.15e-8 s^-1

But that leaves me with two unknowns.
I'm assuming I need to find At, to relate it to the amount electroplated onto the copper, but don't have t.

Still stuck :(

 

[Simon Bridge]

When you use formulas you have to realize what they are for, what they mean.

I was thinking:
At=Ao*e^[-λ*t]
Ao=7340 particles/sec
λ=1.15e-8 s^-1

But that leaves me with two unknowns.

You mean you don't know t and A(t)?
Consider: the problem statement says "immediately after preparation".
What time is that?

So you reckon A(t) is the decay rate at time t?
In which case you need to relate A₀ to the initial number of particles present.

Hint: the decay rate is R=-dN/dt and is directly proportional to the number of particles present.

 

[DMUT]

This equation may be helpful for your question:

$R = \frac{0.693N}{t1/2}$

R = activity, rate of decay
N = number of particles
t1/2 = half-life