What is the Conversion Rate from Curie to Becquerel?

  • Thread starter Thread starter Drizzy
  • Start date Start date
  • Tags Tags
    Ci
Click For Summary
SUMMARY

1 Curie (Ci) corresponds to the decay rate of 1 gram of radium-226, which is approximately 3.7 × 1010 decays per second. To convert Curie to Becquerel (Bq), one must use the formula A = λ * N, where λ is the decay constant and N is the number of atoms. The discussion emphasizes the importance of accurately calculating the initial number of radium atoms, which is derived from its molar mass (226 g/mol) and Avogadro's number (6.022 × 1023 atoms/mol). The correct calculation yields approximately 2.66 × 1021 atoms for 1 gram of radium-226.

PREREQUISITES
  • Understanding of radioactive decay and half-life concepts.
  • Familiarity with the mole concept and Avogadro's number.
  • Basic knowledge of the formula A = λ * N for radioactive decay.
  • Ability to perform unit conversions between grams and atomic mass units (u).
NEXT STEPS
  • Study the principles of radioactive decay and half-life calculations.
  • Learn how to apply the mole concept in chemical calculations.
  • Explore the relationship between Curie and Becquerel for various isotopes.
  • Practice calculations involving Avogadro's number and molar mass conversions.
USEFUL FOR

Students studying nuclear chemistry, physics enthusiasts, and professionals working with radioactive materials who need to understand the conversion between Curie and Becquerel.

Drizzy
Messages
210
Reaction score
1

Homework Statement


1 Curie corresponds to the number of decay in 1 gram radium-226 in 1 second. How many Bequerel is 1 Curie?

Homework Equations

The Attempt at a Solution



Half life: 1600 years

1 gram = 0,001 kg = (0,001/1,660539*10^-27) u
one Radium atom = 226,0260974 u

Number of decays: (0,001/1,660539*10^-27)/226,0260974

Then I thought that since the half-life is so high that the activity won't change much in only 1 second so I though I could pretend that the activity is constant. So I just divided the number of decays with one second but my answer is wrong. In the key that I got from my teacher I am supposed to use this formula: A = lambda * N.

Is it wrong to assume that the activity doesn't change so much in 1 second?
 
Physics news on Phys.org
Drizzy said:

Homework Statement


1 Curie corresponds to the number of decay in 1 gram radium-226 in 1 second. How many Bequerel is 1 Curie?

Homework Equations

The Attempt at a Solution



Half life: 1600 years

1 gram = 0,001 kg = (0,001/1,660539*10^-27) u
one Radium atom = 226,0260974 u

Number of decays: (0,001/1,660539*10^-27)/226,0260974

Then I thought that since the half-life is so high that the activity won't change much in only 1 second so I though I could pretend that the activity is constant. So I just divided the number of decays with one second but my answer is wrong. In the key that I got from my teacher I am supposed to use this formula: A = lambda * N.

Is it wrong to assume that the activity doesn't change so much in 1 second?
Possibly.

But I can't figure out your calculations. 1 g of radium 226 contains a certain number of atoms initially. Even figuring a constant decay rate over the HL of this isotope gives you a much closer figure than the one you didn't finish calculating, BTW.

Remember Avogadro!
 
okay I will try to explain it. 1 g is 0,001 kg. Then I divided it by1,66 * 10^-27 because I want to convert it from kg to u. And then when I have it in u I took it and divided it by how much one atom weighs so that I know how many atoms there are.

My book uses this method at times.. they say that we pretend that the activity is constant when the time is small compared to the half-life so I thought I could apply that to this question too. I don't know why they didn't do it on this question.. is it maybe because we know that the atom is known, that we now tht it is radium and we can calculate A through the formula?
 
Drizzy said:
okay I will try to explain it. 1 g is 0,001 kg. Then I divided it by1,66 * 10^-27 because I want to convert it from kg to u. And then when I have it in u I took it and divided it by how much one atom weighs so that I know how many atoms there are.

You don't care how much an atom of radium weighs, only how many atoms of radium you start with.

You know that 1 mole of Ra-226 will contain a fixed number of atoms, namely Avogadro's number, which is 6.022 × 1023 atoms. You figure out how many moles 1 g of radium is by dividing this amount by the molecular weight of radium, which in this case is 226. The corollary to this is that 226 g of Ra-226 = 1 mole of atoms, by definition.

https://en.wikipedia.org/wiki/Mole_(unit)

My book uses this method at times.. they say that we pretend that the activity is constant when the time is small compared to the half-life so I thought I could apply that to this question too. I don't know why they didn't do it on this question.. is it maybe because we know that the atom is known, that we now tht it is radium and we can calculate A through the formula?
I just don't think you have calculated the initial number of atoms of radium correctly, regardless of what method your book seems to use.
 
my book got 2,66 * 10^21 atoms. if I calculate this:

(0,001/1,660539*10^-27)/226,0260974 I et exactly 2,66 * 10^21 So it seems to be right
 
Drizzy said:
my book got 2,66 * 10^21 atoms. if I calculate this:

(0,001/1,660539*10^-27)/226,0260974 I et exactly 2,66 * 10^21 So it seems to be right

That's the same number as dividing Avogadro by the MW of radium (226). Less fuss using moles.

So, this means that your decay rate is calculated incorrectly. The number which you claim is the number of decays in the OP doesn't seem to use the HL of radium.
 
I don't know how to use moles.

the key= 1 mole Radiums is 226 grams. How am I supposed to know this?
 
never mind i figured it out :) Thanx for helping out :P
 
Drizzy said:
I don't know how to use moles.

the key= 1 mole Radiums is 226 grams. How am I supposed to know this?
By knowing the definition of what a mole is, just like you know what a kilogram is or what a meter is. I even provided a link.

The mole is not some obscure concept. It's what most of chemistry is based on as well as working with the ideal gas laws in physics.

PV = nRT, the n represents the number of moles of gas.
 

Similar threads

Rate of emission of alpha particle in uranium decay
  • · Replies 2 ·
Replies
2
Views
2K
Radioactive decays - given power value
  • · Replies 5 ·
Replies
5
Views
2K
Radioactivity & Specific Heat Capacity Question
  • · Replies 3 ·
Replies
3
Views
3K
Off by order of magnitude when calculating how much calcium is in bone
  • · Replies 8 ·
Replies
8
Views
2K
Calculation on spontaneous fission and effect from alpha decay
  • · Replies 23 ·
Replies
23
Views
2K
Rb-87 Half Life Calculation: 478 Bq/g
  • · Replies 1 ·
Replies
1
Views
2K
Activity of 1 g of carbon if 1 in 10^12 atoms are carbon-14
  • · Replies 11 ·
Replies
11
Views
5K
How can I calculate sieverts from the activity of depleted uranium?
  • · Replies 7 ·
Replies
7
Views
6K
Find N for Isotope with 10.84 Day Half-Life
  • · Replies 5 ·
Replies
5
Views
2K
Age of radioactive sample, single variable equation.
  • · Replies 4 ·
Replies
4
Views
2K