You might be interested in this earlier discussion on this question, which I contributed to.

The long and short is that Chernobyl had very little direct impact on the dissolution of the USSR.

The single most important primary factor in the dissolution are the political reforms that Gorbachev instituted, but which unleashed centrifugal forces that he was unable to control.

The Chernobyl accident arguably played an indirect role in that the accident and governmental response, plus the threat of radiactive waste, convinced Gorbachev of the need to push harder for reforms to the political system and to de-escalate the Cold War. However, it wasn't the primary motivator for him undertaking these reforms (he had mused on the need for reform years previous), and his more radical and far-reaching reforms came a couple years after the accident.