When the tube is filled with mercury vapor, as in this case, a sharp drop in the collected current is observed when the accelerating potential reaches 4.9 VV. The current drops suddenly to a negligible value and slowly increases again when the accelerating potential is above 4.9 VV. What is the energy EEE absorbed by the atomic electrons in the mercury atom when the accelerating potential is 4.9 VV

4.9 eV .

Explanation:

It is the case of discharge through mercury tube light . In it , mercury  atoms are exited due to which electrons are sent to higher energy  level . Here current drops to zero because electrons are excited to higher level . Energy are absorbed in quantised manner . Energy absorbed by electrons will be 4.9 eV . That means , difference in energy  between two energy level is  4.9 eV .

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach