# Quantum Physics - Probabilities

#### jazznaz

23
0
1. The problem statement, all variables and given/known data

A tritium atom is in the ground state and undergoes beta emission, creating a positively charged Helium ion. Assuming the nuclear change is instantaneous and there are no recoil effects, calculate the probability that the Helium ion will be found in its ground state...

2. Relevant equations

None

3. The attempt at a solution

I've already shown that the form of the ground state energy eigenfunction is:

$$\psi (r) = \sqrt{\frac{Z^{3}}{\pi a_{0}^{3}}} e^{-\frac{Zr}{a_{0}}}$$

where Z is the nuclear charge and $$a_{0}$$ is the Bohr radius.

I know that the ground state energy for a hydrogenic atom is $$E_{1}= 13.6$$ eV.

However, despite looking through my notes and a few books, I can't seem to set up the required probability calculation.

Any help or pointers would be very much appreciated.

Last edited:

#### Dahaka14

73
0
I am not exactly sure how I would do this either, but I think I have an idea behind what the question is trying to say. If someone else can spot my reply as being wrong, tell him so I don't point him in the wrong direction. Let me ask you this: how many electrons does tritium have? How many does the helium ion product have then? What does this tell you about the states of helium? Post again if you are still confused!

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