When it orbited the Moon, the Apollo 11 spacecraft’s mass was 14800 kg, and its mean distance from the Moon’s center was 1.79877 × 106 m. Assume its orbit was circular and the Moon to be a uniform sphere of mass 7.36 × 1022 kg. Given the gravitational constant G is 6.67259 × 10−11 N m2 /kg2 , what is the minimum energy required for the craft to leave the orbit and escape the Moon’s gravitational field?

Explanation:

If M be mass of moon and m be mass of spacecraft

potential energy of moon -spacecraft system

= - G M m / R where R is radius of orbit of spacecraft

kinetic energy of spacecraft in the orbit

= 1/2 m v² = GMm / 2R

Total energy of spacecraft

=  GMm / 2R  - G M m / R

= - GMm / 2R

for spacecraft to leave the orbit,  energy required

= GMm / 2R

= 6.67259 x 10⁻¹¹ x  7.36 x 10²² x 14800 / (2 x 1.79877 x 10⁶)

= 202035.8 x 10⁵ 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.