The concept you're referring to is known as a runaway or uncontrolled chain reaction, where the splitting of atoms through nuclear fission becomes self-sustaining and uncontrollable. However, it's important to note that the likelihood of such a scenario occurring depends on various factors, including the specific isotopes involved, their concentrations, the design of the nuclear reactor, and the control mechanisms in place.
In practice, nuclear reactors are designed with multiple safety features and control systems to prevent uncontrolled chain reactions. These include control rods that absorb neutrons, which are used to regulate the fission process, and safety systems that can shut down the reactor if necessary.
The number of times an atom can be split before an uncontrolled chain reaction occurs is highly dependent on the conditions mentioned above and cannot be generalized. In a properly designed and operated nuclear reactor, the splitting of atoms occurs in a controlled manner, with each fission event leading to the release of more neutrons that go on to cause subsequent fission reactions. This is known as a controlled chain reaction, which allows for the sustained production of energy.
However, if the conditions for control are lost, such as the failure of safety systems or an unintended criticality event, an uncontrolled chain reaction could potentially occur. In such a situation, the number of times an atom can split before an explosion would depend on the specific circumstances and characteristics of the nuclear material involved.
It's important to note that uncontrolled chain reactions leading to explosions are extremely rare and highly unlikely to occur in properly designed and operated nuclear facilities. Stringent safety protocols and multiple layers of containment are in place to prevent such incidents and ensure the safe operation of nuclear reactors.