Nuclear Physics for AP Physics B- Equations to be Remembered

Nuclear physics is supposed to occupy just 3% of the total content of the syllabus for the AP Physics B (2009) Examination. However you need to remember the following things in this section for answering the questions within the stipulated time:

(1) Mass number (A) is the number of nucleons (neutrons & protons) and is given by

A = Z + N

where Z is the atomic number (number of protons in the nucleus) and N is the neutron number.

Isotopes have same Z but different A.

Isotones have same N.

Isobars have same A but different Z

Isomers have same A and same Z but different nuclear energy states

(2) Nuclear radius (size) R is given by

R =R₀A^1/3

where R₀ = 1.2×10^–15 m. The volume of the nucleus which is proportional to R³ is therefore proportional to the mass number A. This means that the density of the nucleus is constant (approximately 2.3×10¹⁷ kgm^–3) and is independent of A.

(3) Einstein’s mass-energy equivalence relation is

E = mc²

where E is the energy (in joules) obtained on annihilating a mass m kg and c is the speed of light in free space.

(4) Mass defect ∆M is the difference between the mass of the nucleus and the total mass of its constituents(nucleons):

∆M = [Zm_p + (A–Z)m_n] – M

where m_p is the mass of the proton, m_n is the mass of the neutron and M is the mass of the nucleus.

The binding energy E_b of the nucleus is given by

E_b = ∆M c²

The binding energy per nucleon is E_b/A

(5) Three types of radioactive decay occur in nature.They are:

(i) α-decay in which an α-particle (helium nucleus ₂He⁴) is emitted;

(ii) β-decay in which electrons or positrons are emitted;

(ii) γ-decay in which γ-rays (high energy photons) are emitted

When an α-particle is emitted by a nucleus its mass number decreases by 4 and its atomic number decreases by 2.

When an electron is emitted by a nucleus (β^– decay) its mass number is unchanged but its atomic number increases by 1.

When a positron is emitted by a nucleus (β⁺ decay) its mass number is unchanged but its atomic number decreases by 1.

When a γ-ray photon is emitted by a nucleus its mass number and atomic number remain unchanged.

In β^– decay a neutron within the nucleus gets transformed into a proton in accordance with the relation,

n→ p + e^– + ν where n, p, e^– and ν represent the neutron, proton, electron and the antineutrino respectively.

In β⁺ decay a proton within the nucleus gets transformed into a neutron in accordance with the relation,

p→ n + e⁺ + ν where e⁺ and ν represent the positron and the neutrino respectively.

(6) In nuclear fission reaction a heavy nucleus such as ₉₂U²³⁵ or ₉₄Pu²³⁹ absorbs a slow neutron and breaks into two fragments of nearly equal size, releasing large amount of energy (typically about 200 Mev per fission). Two or three neutrons also are produced in the reaction. A typical example of fission reaction is

₀n¹ + ₉₂U²³⁵→ ₉₂U²³⁶→ ₅₆Ba¹⁴¹ + ₃₆Kr⁹² + 3 ₀n¹

Fragments other than barium and krypton can be produced in the reaction.

(7) In nuclear fusion reaction two light nuclei combine to form a single larger nucleus with release of energy. A common example of nuclear fusion reaction is the one given below in which two deuterons combine to form the light isotope of helium:

₁H² + ₁H² → ₂He³ + ₀n¹ + 3.27 Mev

You should remember that the total mass number on the left hand side should be the same as that on the right hand side of the equations representing the nuclear reaction. Similarly the charge numbers also should match.

Questions for high lighting the above facts and the law of conservation of energy and momentum are often asked in degree entrance examinations.