A qualitative argument is to consider the energy uncertainty of an electron

The characteristic time for charge fluctuations is

the time constant for charging capacitance *C* through tunnel resistor *R*_{T},
and the energy gap associated with a single electron is

Combining (2.26) and (2.27) gives the condition for the
tunnel
resistance

Another line of thought proceeds as follows. The condition
requires that the time *t* which an electron
resides on the island be much greater than ,
the quantum uncertainty
in this time.

The current *I* cannot exceed *e*/*t* since for moderate bias and temperature
at most one extra electron resides on the island at any time. The
energy uncertainty of the electron, ,
is no larger than the
applied voltage *V*_{b}.

Inserting *t*=*e*/*I* and (2.30) into (2.29) results in

In fact, more rigorous theoretical studies of this issue have supported this conclusion [111]. Experimental tests have also shown this to be a necessary condition for observing single-electron charging effects [39].