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

[Lachlan1]

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

 

[phyzguy]

You need the energy numbers to calculate the activity. Do you know the definition of a Curie (Ci)?

 

[Lachlan1]

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