# Homework Help: Why there is no isotope of hydrogen with an atomic weight of four?

1. May 19, 2008

### estrella

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

2. Relevant equations
why there is no isotope of hydrogen with an atomic weight of four?

3. The attempt at a solution
i find that such an isotope would have an isotopic spin state of 1/2 |2-1> + 3/2 |1 -1>
is there a reason for this state to not exist?

Last edited: May 19, 2008
2. May 19, 2008

### jsc314159

Do you mean hydrogen with a nucleus of 1 proton and 3 neutrons?

Tritium is a radioactive isotope of hydrogen with 1 proton and 2 neutrons. It usually decays via
$$H^3 -> (He^3)^+ + e^- + \nu^-$$

Perhaps $$H^4$$ would be unstable due to internuclear forces.

jsc

3. May 19, 2008

### estrella

yes. I want to explain why a nucleus of 1 proton and 3 neutrons does not exist by using the isospin.
so i thought i should calculate the isospin of the combination n+n, then the combination p+n and then combine the results to find the isospin of the nucleus.
i assume that i sould find an unreasonable result to explain why it doesn't exist.
Any idea?

4. May 20, 2008

### reilly

There are no restrictions, other than that supplied by the Pauli Principle, on isospins of any set of protons and neutrons. Why would there be?

Why would Nature allow Helium 4, but not Hydrogen 4?
Regards,
Reilly Atkinson

5. May 21, 2008

### estrella

i did my research on the subject and you are wright reilly.
thanks!