Questions on radioactivity and early earth atmosphere.

My Astronomy text likes to ask questions that make us ‘think outside the box.’ Unfortunately, they don’t have answers, so I have no idea if I am on the right track or way off.

One of the questions is: Would the heat-production rate from radioactivity when the Earth formed have been more, less or the same as it is now?

My WAG: The rate would be lower because as the elements decayed they would give off less radioactivity with each half life. For example, uranium-238 has a half life of 4.51 billion years. That means that now, there are at least half as many u238 as there were when the Earth was formed. Since there are only half, there is half as much radioactivity being given off by them.

Am I even close?

The second question: What happened to the abundant hydrogen atoms initially present or produced by the breakup of molecules such as methane.

My WAG: I am assuming that the Hydrogen joined with Oxygen and became water since we have so much of it. But I feel like that isn’t the full answer.

So is there more to it or is that just basically it?

Thanks for your help!

Much of the hydrogen escaped to space

How/why did it escape into space? Because the atmosphere wasn’t in place? Does is still escape to this day?

It escaped because hydrogen is light enough that the motion induced by heating exceeds the escape velocity of the Earth. The same reason why oxygen can and does escape from the moon’s gravity.

Yes, it still escapes today as does helium.