Alpha decay short half lives correspond to large disintegration energies

[dm9292]

Homework Statement

i) Explain why in alpha decay short half lives correspond to large disintegration energies.

ii) Determine the energy release during the alpha decay of ²³⁸U to ²³⁴Th. The mass of ²³⁸U is 238.0508m_u, the mass of ²³⁴Th is 234.0436m_u, and the mass of ⁴He is 4.0026m_u.

Homework Equations

None Given

The Attempt at a Solution

I haven't seen an example of this in my course book, so I have more ideas than attempts at a solution.

Would I be right in right in finding the mass defect in U, Th and He, and then subtracting U's mass defect from Th's and He's, mass defect.

Once I have that I would use E=mc², to calculate the energy released.

But this seems quite long and drawn out is there another method to calculate this, is the method even right?

 

[Hao]

You have the right idea for ii). What you mention is essentially conservation of relativistic energy, and it doesn't get much simpler than that.

A partial answer to i) would be to consider the conditions under which the probability of tunneling out of a potential barrier increases, and see how that is relevant to alpha decay.