When some stars use up their fuel, they undergo a catastrophic explosion called a supernova. this explosion blows much or all of a star's mass outward, in the form of a rapidly expanding spherical shell. as a simple model of the supernova process, assume that the star is a solid sphere of radius r that is initially rotating at 2.4 revolutions per day. after the star explodes, find the angular velocity, in revolutions per day, of the expanding supernova shell when its radius is 4.3r. assume that all of the star's original mass is contained in the shell.

0.0768 revolutions per day

Explanation:

R = Radius

= Angular velocity

As the mass is conserved the angular momentum is conserved

Moment of intertia for solid sphere

Moment of intertia for hollow sphere

Dividing the moment of inertia

From the first equation

The angular velocity, in revolutions per day, of the expanding supernova shell is 0.0768 revolutions per day

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.