Hello,

Not all hydrogen atoms have zero neutron.

There are three isotopes of Hydrogen i.e

1. Hydrogen ( ¹ H)
2. Deuterium ( ² H)
3. Tritium ( ³ H)

Hydrogen ( ¹ H) has just one proton in nucleus and no neutron. Deuterium ( ² H) has one proton and one neutron in its nucleus.Tritium ( ³ H)  has one proton and two neutrons in its nucleus making it radioactive while the first two isotopes are stable.

Hydrogen( ¹ H) does not have neutrons but only one protonas it is is stable because there is no interaction attempting to blow the nucleus apart.

In Deuterium ( ² H)  there is one neutron and one proton so the nucleus doesn't blow apart because of weak interactions.

Tritium ( ³ H) has two neutrons and one proton making it unstable as well as radioactive due to strong interactions.

Hope this was helpful.