How much energy is emitted in each α decay of plutonium-234? (234Pu, 234.0433mu; 230U, 230.0339mu; 4He = 4.0026 mu).

I tried finding the difference in mass first:

(230.0339 + 4.0026) - (234.0433) = -.0068 mu

I then converted from amu to kg by multiplying by 1.6605E-27. Then (using E=mc^2) i multiplied by (3E8)^2 to get 1.016E-12 J

to find how many J are emitted per decay I multiplied the above by (1E-3 kg over the mass of Pu-234 in kg) to get -2.615E9 J

This is however, incorrect and I don't know what step I am doing wrong...haven't been able to get a hold of my professor...Thanks!

Dr. Bob if you see this...I also had a question on my earlier posting (sorry I don't know how to type in the sub/super scripts...)..

Nevermind...I realized that the problem I was using as an example called for 1 g of the reactant used....this didn't....so I have my correct answer now. Thanks!

Still stumped on my earlier question though...

I think I've answered that in an earlier response. I think you are looking at a neutron.

you have the right answer but don't factor in one gram of substance, it wants the amount per alpha decat there are alot of alpha decays in a gram.

So it is just 1.016E-12

To calculate the energy emitted in each α decay of plutonium-234 (234Pu), you need to consider the difference in mass before and after the decay and use the equation E = mc^2, where E is the energy, m is the mass difference, and c is the speed of light.

Let's go through the calculation step by step:

1. Find the mass difference:
The mass of the daughter nucleus, uranium-230 (230U), and helium-4 (4He) are given, so we can calculate the mass difference:
Mass difference = (230.0339 mu + 4.0026 mu) - 234.0433 mu
= 234.0365 mu - 234.0433 mu
= -0.0068 mu

Note: mu represents atomic mass units (amu).

2. Convert mass difference to kilograms:
To use the equation E = mc^2, you need to convert the mass difference from atomic mass units to kilograms. Multiply the mass difference in atomic mass units by the conversion factor 1.6605 × 10^-27 kg/amu:
Mass difference (kg) = -0.0068 mu * (1.6605 × 10^-27 kg/amu)
= -1.1294 × 10^-29 kg

3. Calculate the energy using E = mc^2:
Multiply the mass difference in kilograms by the square of the speed of light, c, which is approximately 3 × 10^8 m/s:
Energy (J) = (-1.1294 × 10^-29 kg) * (3 × 10^8 m/s)^2
= -1.0165 × 10^-12 J

Note: The negative sign arises because the energy is released during the α decay.

So, the correct energy emitted in each α decay of plutonium-234 is -1.0165 × 10^-12 J, or approximately -1.02 picajoules (pJ).

If you have any other questions or need further clarification, feel free to ask!