VISUAL PHYSICS ONLINE

8.2 FROM THE UNIVERSE TO THE ATOM

THE NUCLEUS

P82 002

Discuss the connection between natural radioactivity and Einstein’s famous mass/energy equation.

View solution below only after you have completed the answering the question.

Solution

There are three kinds of natural radiations, alpha particles a, beta particles b and gamma rays g that are emitted from a nucleus of an unstable atom.

Alpha decay

An alpha particle (a particle) is a helium nucleus ⁴He₂ that is naturally emitted from an unstable nucleus producing a nucleus of a new element.

Emission of a ⁴He₂ nucleus: N → (N – 2) Z → (Z – 2) A → (A – 4)

Transmutation of a parent P into its daughter D:

^AP_Z ® ^A-4D_Z-2 + ⁴He₂

Example radium ® random + a

²²⁶Ra₈₈ ® ²²²Rn₈₆ + ⁴He₂

²²²Rn₈₆ ²²⁶RN₈₈ ⁴He₂

Mass (parent) > Mass (products)

Mass defect Dm = Mass(parent) – Mass(products)

Kinetic energy of products is due to the mass defect (from E = m c²)

KE(products) = Dm c²

Beta decay occurs when a nucleus has either too many or too few neutrons relative to the number of protons present for stability. Stability can be achieved by the conversion inside the nucleus of a proton into a neutron or a neutron into a proton. In this transmutation:

Charge is conserved Þ a beta particle (b⁺ or b^-) is emitted from the nucleus

Energy and momentum are conserved Þ

A particle called a neutrino (n_e or ) must also be emitted from the nucleus.

Greek letter nu (n)

Reduction of a neutrons & increase in a proton inside nucleus N / Z too large

N → N – 1 Z → Z + 1 A → A

^AP_Z ® ^AD_Z+1 + e^- +

¹⁴C₆ ® ¹⁴N₇ + e^- +

Mass (parent) > Mass (products)

Mass defect Dm = Mass(parent) – Mass(products)

Kinetic energy of products is due to the mass defect (from E = m c²)

KE(products) = Dm c²

Gamma rays (g rays) are photons having very high energy that were emitted from excited nuclei, much like emission of photons by excited atoms. Like an atom, a nucleus itself can be in an excited state. When it jumps down to a lower energy state it emits a photon called a g ray. The energy level separations in a nucleus (~ MeV) are much greater than the energy level differences in an atom (~ eV). For a given decay, the g ray always has the same energy and since the photon is electrically neutral, there is no change in the element as a result of the decay.

· Gamma rays are extremely high frequency (short wavelength) electromagnetic waves where the photons are emitted from excited nuclei.

· N, Z and A do not change

A nucleus can be in an excited state after it suffers a violent collision with another particle, or more commonly the daughter nucleus remaining after an a decay or b decay is left in an excited state.

²²⁶Ra₈₈ ® ²²²Rn₈₆^* + ⁴He₂ energy of a particle 4.685 MeV

²²²Rn₈₆^* ® ²²²Rn₈₆ + g energy of g ray 0.186 MeV

The energy of the emitted gamma ray is due to the decrease in mass in the gamma emission process: mass ® energy as given by E = m c²