The energy required to start an electron cascade may come from the applied electric field if it is too large. Ideally the applied field will be close to but not quite enough to trigger a discharge in the ionization chamber. Then when an external source of energy comes along, like a gamma ray for example, it will add enough energy to set off the cascade and cause a pulse of current through the ionization chamber. In this way the incoming gamma ray may be detected.
Your question comes down to calculating the maximum electric field for the ionization chamber geometry given in the problem, as a function of the applied potential difference. Then setting that field function equal to the given dielectric strength of the gas filling the tube. Solving that equation for the potential difference will give you an answer.
This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.
JDJ