The Nucleus Physics - The Nucleus

A free neutron beta-decays to a proton with a half-life of 14 minutes.

1. What is the decay constant?
2. Find the energy liberated in the process.

In the decay ⁶⁴Cu → ⁶⁴Ni + e⁺ + v, the maximum kinetic energy carried by the positron is found to be 0.650MeV.

1. What is the energy of the neutrino which was emitted together with a positron of kinetic energy 0.150MeV?
2. What is the momentum of this neutrino in kg-m/s?

Use the formula applicable to a photon.

Calculate the energy released by 1g of natural uranium assuming 200MeV is released in each fission event and that the fissionable isotope ²³⁵U has an abundance of 0.7% by weight in natural uranium.

Consider the situation of the previous problem. Suppose the production of the radioactive isotope starts at t = 0. Find the number of active nuclei at time t.

If three helium nuclei combine to form a carbon nucleus, energy is liberated. Why can't helium nuclei combine on their own and minimise the energy?

A uranium reactor develops thermal energy at a rate of 300MW. Calculate the amount of ²³⁵U being consumed every second. Average released per fission is 200MeV.

The half-life of a radioisotope is 10h. Find the total number of disintegrations in the tenth hour measured from a time when the activity was 1Ci.

Calculate the minimum energy needed to separate a neutron from a nucleus with Z protons and N neutrons it terms of the masses M_Z.N, M_Z,N-1 and the mass of the neutron.

The half-life of ²²⁶Ra is 1602y. Calculate the activity of 0.1g of RaCl₂ in which all the radium is in the form of ²²⁶Ra. Taken atomic weight of Ra to be 226g/mol^-1 and that of Cl to be 35.5g/mol^-1.

Ten grams of ⁵⁷Co kept in an open container beta-decays with a half-life of 270 days. The weight of the material inside the container after 540 days will be very nearly:

1. 10g
2. 5g
3. 2.5g
4. 1.25g

The mass of a neutral carbon atom in ground state is:

1. Exact 12u
2. Less than 12u
3. More than 12u
4. Depends on the form of carbon such as graphite or charcoal.

As compared to ¹²C atom, ¹⁴C atom has:

1. Two extra protons and two extra electrons.
2. Two extra protons but no extra electron.
3. Two extra neutrons and no extra electron.
4. Two extra neutrons and two extra electrons.

The mass number of a nucleus is:

1. Always less than its atomic number.
2. Always more than its atomic number.
3. Equal to its atomic number.
4. Sometimes more than and sometimes equal to its atomic number.

4 × 10²³ tritium atoms are contained in a vessel. The half-life of decay tritium nuclei is 12.3y. Find:

1. The activity of the sample.
2. The number of decay in the next 10 hours.
3. The number of decays in the next 6.15y.

In beta decay, an electron (or a positron) is emitted by a nucleus. Does the remaining atom get oppositely charged?

A neutron star has a density equal to that of the nuclear matter. Assuming the star to be spherical, find the radius of a neutron star whose mass is 4.0 × 10³⁰kg (twice the mass of the sun).