Ok.. put it this way, for a hydrogen atom to lose energy is much less in statistical significance to a ground state to gain bonds. The reason why is because ... in a loose sense of the terminology we tend to use, would take an infinite amount of energy for a ground state particle to decay.
That's why this is an approximation, I am not going to take the time to calculate the hundreds of complex factors that would give rise to this as it would take me months to solve. I understand that they can not actually decay the hydrogen atoms but it is the math curve I was trying to fit this to rather than do that HUGE calculation to exactly get your answer. I will leave something like that to the OP.
Edited by VictorMedvil, 14 May 2019 - 05:29 PM.