Basic Nuclear Decay: Calculating Min Mass for 10Ci in 30 Months

In summary, to calculate the activity of 60Co after 30 months, you need the decay constant and the rate of decay.
  • #1
Lachlan1
21
0

Homework Statement



60Co, half life = 5.2 years, decays by emittion of a beta particle (0.31 MeV) and two gamma particles (1.71MeV and 1.33MeV). what is the minimum initial mass needed of 60Co that will have an activity of at least 10Ci after 30 months?

Homework Equations


half life = ln(2)/decasy constant(λ).
Amount of nuclei (N) = rate of decay(R)/decay constant(λ).
N=N(starting) x e^(-λ)(t)
in this equation t is the time between the starting amount and the amount, N, left after the decay.


The Attempt at a Solution



so, i am reasonably competent at the simpler problems involving these formulas, just plug the number in basically. But for this one, i am a little unsure how to include the energy numbers. they don't normally put numbers in if they are not needed.
i can calculate a number which is the amount of nuclei needed to start with, when you have the decay rate they given, and time (i got 1.222x10^20). but this is not the mass.

so I am thinking i must have to use the energy in decay with the nuclei number to calculate the mass maybe. or is there a way i can go straight from the number of nuclei to the mass that i am missing? any thoughts would be helpful. thanks
 
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  • #2
You need the energy numbers to calculate the activity. Do you know the definition of a Curie (Ci)?
 
  • #3
Thanks. Yes i know the defnintion of the Ci, it is 3.7x10^10 Bq.
with the half life, i calculatd the decay contant.
with know time, activity and decay constant, i can calculate the initial amount, No.
With the initial amount No and the decay constant, i can find the initial activity.
unless this process is incorrect. arent the energies redundant? With what equation would i use the energies to calculate the rate anyway, i am not sure how this would be done?

thanks again
 

1. What is nuclear decay?

Nuclear decay, also known as radioactive decay, is the process by which an unstable atomic nucleus loses energy in the form of radiation and transforms into a more stable nucleus. This process can occur naturally or can be induced in a laboratory setting.

2. How is nuclear decay measured?

Nuclear decay is typically measured in units of Becquerels (Bq) or Curie (Ci). Becquerels represent the number of nuclear decays per second, while Curie represents the number of nuclear decays per second per gram.

3. What is the significance of calculating the minimum mass for a given amount of radioactivity?

Calculating the minimum mass for a given amount of radioactivity is important in determining the amount of material needed to produce a certain level of radiation. This information is useful in ensuring the safety of workers and the public in situations where radioactive materials are present.

4. How do you calculate the minimum mass for a given amount of radioactivity?

The minimum mass for a given amount of radioactivity can be calculated using the formula: Minimum Mass = (Activity in Curie * Half-life in seconds)/3.7*10^10. This formula takes into account the specific activity of the radioactive material and the time frame in which the activity will be present.

5. What are the factors that affect the rate of nuclear decay?

The rate of nuclear decay can be affected by several factors, including the type of radioactive material, its half-life, and its environment. Additionally, external factors such as temperature, pressure, and radiation exposure can also influence the rate of nuclear decay.

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