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

## Homework Equations

why there is no isotope of hydrogen with an atomic weight of four?

## 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?

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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

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?

reilly