The voltage through a capacitor can't change instantaneously, so immediately after the switch is closed, the potential difference will keep at 100 V.
This voltage will produce a flow of charge (a current) from the capacitor to the resistor, which will be diminishing continuously, till the capacitor be totally discharged, and the current becomes zero.
The voltage through the capacitor will follow an exponential function of time, as follows:
Replacing by the givens in (1):
Taking ln on both sides in (2), and solving for RC, we have:
So, the time constant of the circuit (the product of R times C) is equal to 2.17s.
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