the planet express is in a circular orbit around the earth and has a total mechanical energy of -4.6 x 10^10 j. how much work must be provided by the planet expresss rockets in order to completley escape earth

 total mechanical energy of -4.6 x 10^10 j. 

Explanation: the planet express is in a circular orbit around the earth and has a total mechanical energy of -4.6 x 10^10 j.

The total mechanical energy is the sum of potential energy and the kinetic energy.

For the rocket to experience the escape from earth, the total work done will be equal to maximum kinetic energy.

According to conservative of energy, maximum kinetic energy is equal to the total mechanical energy.

The work must be provided by the planet expresss rockets in order to completley escape earth will be equal to  total mechanical energy of -4.6 x 10^10 j. 

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.