A gold nucleus (with a radius of 6.5 fm in its rest system, containing 197 protons and neutrons of rest mass 939 MeV/c2 each) is accelerated to a speed of 0.97 c. Calculate (a) the momentum of an individual nucleon (ignoring binding energy effects). (b) the total energy of the gold nucleus, including its binding energy of 7.9 MeV per nucleon. (c) the diameter of the gold nucleus in the direction of motion as seen by an observer at rest.

762474.685899 MeV

3.1603639031 fm

Explanation:

v = 0.97 c

c = Speed of light =

Relativistic momentum is given by

The momentum is

Energy in MeV

Total energy is

The total energy is 3870.42987766 MeV

For all the nucleons

The energy is 762474.685899 MeV

Diameter =

From length contraction

The diameter would be 3.1603639031 fm

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.