- #1

- 48

- 9

- Homework Statement
- In α decay of Ra(A=226,Z=88) (at rest initially) : Ra radiates 3.7×10^10 α nuclei.The kinetic energy of an α nucleon is 4.78 MeV and the ratio between the mass of α and one of the daughter nucleon is mα/mdaughter =0.018.

The reaction energy is:

a) 2.88×10^-2 J

b) 50×10^-2 J

c) 30×10^-3 J

d) 0.85 J

- Relevant Equations
- Conservation of momentum

p1 + p2 = p3 + p4

Reaction energy

W= (M.initial - M.final)x c^2

Relation between momentum and kinetic energy

p^2 = 2mK

I tried momentum conservation, which gives:

-pα = pdaughter

<=> 2mKα = 2mKdaugther (squaring two sides)

Using the given mass ratio, I found Kdaughter to be 0.0864MeV

Adding the two Kinetic energy of the product particles and converting it to Joules, I got A

But I don't understand why adding the two kinetic energy of the product particles would yield the reaction energy (or does it? I'm not even sure I'm doing right, I just happen to get one of the numbers in the answers). The reaction energy is given by a different formula I put under the conservation of momentum formula and I don't think it says "add the two Kinetic energy together".

-pα = pdaughter

<=> 2mKα = 2mKdaugther (squaring two sides)

Using the given mass ratio, I found Kdaughter to be 0.0864MeV

Adding the two Kinetic energy of the product particles and converting it to Joules, I got A

But I don't understand why adding the two kinetic energy of the product particles would yield the reaction energy (or does it? I'm not even sure I'm doing right, I just happen to get one of the numbers in the answers). The reaction energy is given by a different formula I put under the conservation of momentum formula and I don't think it says "add the two Kinetic energy together".