Calculating Decay Constant and Amount of Thorium Plated

• P1nkButt3rflys
In summary: Use this equation to find N, then use that value to find the amount of thorium electroplated onto the copper.
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?

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!

i.e. what proportion of the alphas emitted are counted?

1 person
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.

1 person
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?

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

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

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

1 person
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 :(

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.

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

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

Last edited:
1 person

1. What is the decay constant of thorium?

The decay constant of thorium is a constant value that represents the rate at which the radioactive material decays. It is denoted by the symbol λ and is typically measured in units of inverse time, such as per second or per year.

2. How is the decay constant of thorium calculated?

The decay constant of thorium can be calculated using the formula λ = ln(2)/t1/2, where ln(2) is the natural logarithm of 2 and t1/2 is the half-life of thorium. The half-life is the amount of time it takes for half of the radioactive material to decay.

3. What is the half-life of thorium?

The half-life of thorium is approximately 14.05 billion years. This means that it takes 14.05 billion years for half of the initial amount of thorium to decay into other elements.

4. How is the amount of thorium plated calculated?

The amount of thorium plated can be calculated using the formula A = A0e-λt, where A is the amount of thorium plated at a given time t, A0 is the initial amount of thorium plated, and e is the mathematical constant approximately equal to 2.71828. This formula takes into account the decay constant and the time elapsed since the initial plating.

5. Is there a way to speed up or slow down the decay of thorium?

No, the decay of thorium is a natural and spontaneous process that cannot be manipulated. The decay constant and half-life of thorium are fixed values that do not change under any external influences.

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