Calculating Carbon Decay: Kinetic Energy, Mass, and Activity

[theleftlane]

Homework Statement

The radiocarbon in our bodies is one of the naturally occurring sources of radiation. Let's see how large a dose we receive. 14C decays via Beta- emission, and 18% of body mass is Carbon.

A) Write out the decay scheme of carbon-14 and show the end product. (A neutrino is also produced.) I got this correct: ¹⁴₆C--> e- + ¹⁴₇N + v_e

B) Neglecting the effects of the neutrino, how much kinetic energy (in MeV) is released per decay? The atomic mass of C-14 is 14.003242 mu.
I honestly don't know how to go about this one at all. I've reread the section this problem comes from and I don't even see a formula that could begin to solve this.

C) How many grams of carbon are there in a 77.0 kg person?
I got this correct. I multiplied 77000g * .18 which =13900g

D) How many decays per second does this carbon produce? (Hint: Assume activity of ¹⁴C is about 0.255 Bq per gram of carbon.)
I've tried this multiple different ways now. For the most part I've started by taking 13900g/14*6.022*10²³ which should give me the N and then I've multiplied that by .255. The equation I used was -lambda*N=deltaN/deltat. As I am looking for decays per second (deltaN/deltat) I don't know how else to go about this.

Homework Equations

deltaN/deltat=-lambda*N
1Bq=1decay/s
N=N₀*e^-lambda*t
T_1/2=ln/2

The Attempt at a Solution

Shown above.

 

[NobodySpecial]

B - you need either the mass of 14N, or you need to just lookup the energy of this decay step

D - the decay is given in Bq per gram of carbon, not per atom

 

[theleftlane]

Thanks a bunch! I'll work on it!

 

[NobodySpecial]

D is much simpler than you think
"Assume activity of 14C is about 0.255 Bq per gram of carbon"
means there are 0.255 decays per gram of carbon / second - you have worked out how much carbon is in the body, and you want the total decays per second!

 

[phyzguy]

Don't forget that most of the carbon in your body is C-12. Only a small fraction (which you can look up) is C-14.

 

[NobodySpecial]

Don't forget that most of the carbon in your body is C-12. Only a small fraction (which you can look up) is C-14.

I think that is taken into account in the decay rate given
The half life of C14 is around 5500yr, so 1.7E11 seconds and 10E23 atoms would give a lot more than 0.255Bq if it was just for the C14

 

[phyzguy]

You're right. Sorry.

 

[NobodySpecial]

You're right. Sorry.

That was my first answer as well before I ran the numbers!
Especially because I got Bq mixed up with the Curie which is a lot larger.