Yes, the stars going supernova will have impact on allowing life to exist in nearby planets.
When a star goes supernova, a large amount of radiation is emitted. So, if a nearby planet inhabiting life has a ozone layer, it will be depleted. This results in increased harmful radiation levels on the ground. There will be mutations in organisms that can survive the radiations. Those that are not strong will die.
A supernova is the explosion of a star. This phenomenon happens when a star's nuclear fuel in its core runs out. As a result the pressure created by the burning in its core becomes completely null. Thus the gravity is only force acting, so the star collapses on itself emitting huge quantities of light and harmful radiation.
Therefore, the stars going supernova will have impact on allowing life to exist in nearby planets.
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