How to get activity of 1g of radium 226?

[hermtm2]

Hello.

I am taking Neculear Power Resource Engineering 402.
The one of the homework is to calculate
activity of 1g of radium 226 as Becquerel and Curie unit?
Can you guys give an equation to me?

Thanks.

 

[Astronuc]

From the mass of Ra 226, one can determine the number of atoms. Then one may use the definition of activity, which is:

A = λN, where λ is the decay constant, and N is the number of atoms.

λ can be determined from the half-life, if it is not already know.

A can be written in decays, or disintegrations per sec, dps, and one should know the value of Ci in dps.

 

[hermtm2]

"A can be written in decays, or disintegrations per sec, dps, and one should know the value of Ci in dps. "

λ = ln(2)/T(1/2)
N = 226 amu

What does the last sentence mean?Thanks.

 

[Astronuc]

N = Number of atoms = Avogadro's number divided by atomic mass. Afterall, atomic mass is just the mass (in grams) of matter in a mole or 6.022 E23 atoms.

If λ is given in s^-1, then A has units of decays, or disintegrations, per second.

There is a definition of Curie (Ci) in units of disintegrations per sec.

 

[hermtm2]

T(1/2) = 1600 years
λ = ln(2)/T(1/2) = 0.000433
N = 6.022*10e23/226 = 2.6646e21

A = λN = 1.15435e18 curie.

Am I on the right track?

Thanks.

 

[theCandyman]

Be sure to write in your units so that you can stay consistent. Your kept your half-life in years so what units would your decay constant be?
1 curie has a value of a certain number of decays/sec. You should look it up, and see what else you can find about where it came from, it will help answer this question.

 

[Astronuc]

T(1/2) = 1600 years
λ = ln(2)/T(1/2) = 0.000433
N = 6.022*10e23/226 = 2.6646e21

A = λN = 1.15435e18 curie.

Am I on the right track?

With the half-life given in years (as indicated by theCandyman), the decay constant would be given in 1/yr or yr^-1. How many seconds in 1600 years?

 

[hermtm2]

I see what the half-life unit should be.
But here is another question: What is the unit of λ and N each?

The question specifically ask 1g of radium, so where can I get the gram unit?
Also the formula in my textbook shows A(t)=λN(t). How do I define the "t" without given time from the original question?

What I am guessing is that the unit of curie is defined by sec. Is that right?

Thanks.

 

[Astronuc]

Activity A has units of decays (or disintegration) per unit time, where the unit time is usually in seconds.

The decay constant λ has units of per unit time, usually 1/s or s^-1.

N or N(t) is just the number of atoms present at a given time t. There is one decay per atom.


A = dN(t)/dt = λ N(t), which is a first order differential equation.

Reference:

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/halfli2.html

Caution - the hyperphysics site use A for the amount of radioactive material, so don't get confused.


In the problem, one is 'given' 1 gram of Ra-226. That's an arbitrary input to the problem.

One uses the fact that the atomic mass 226 means that there are 226 grams of Ra-226 in a gram-mole (mole) of Ra, and there are 6.022 E23 atoms of any substance in a gram mole, so

1 gram yields (6.022 E23 atoms/g-mole )/ (226 g/g-mole) = 2.6646 E21 atoms of Ra-226. One is on the right track.

1 Ci = 3.7×10¹⁰ decays per second or becquerels. 1 Bq = 1 decay per s

 

[QuantumPion]

Isn't this kind of a trick question? I thought 1 curie was defined as the activity of 1 gram of radium

 

[gmax137]

Isn't this kind of a trick question? I thought 1 curie was defined as the activity of 1 gram of radium

Yeah, but the point of the exercise is to show you know what log(2) and Eva Gardner's number mean, to see how it all fits together.

The problem could be re-written:
What's the activity of one gram Ra-226
"easy - one curie!"

OK, what's the 1/2 life of Ra-226?
"Ummmmm...

 

[Astronuc]

Isn't this kind of a trick question? I thought 1 curie was defined as the activity of 1 gram of radium

The OP needs to calculate it.

 

[hermtm2]

Now I see.

Thanks guys.

 

[theCandyman]

Ahhh, you gave him the answer, Quantum!

 

[HotCells]

Use the Mass Activity Calculator in Nucleonica (www.nucleonica.net, requires registration).
Information on this module can be found on the Nucleonica wiki page at...
http://www.nucleonica.net/wiki/index.php/Help:Mass_Activity_Calculator

However, be careful! This is the activity for the pure Ra-226 parent only. In practice there will be a number of daughter products in "equilibrium" with the parent. These effects can be analysed using Nucleonica's Decay Engine (the wiki page is at...
http://www.nucleonica.net/wiki/index.php/Help:Decay_Engine).

Even after only 1 year, the activitiy of an initially pure Ra-226 sample will be around 2.2E11 Bq, i.e. a factor five higher than that of the parent alone.