Atomic Structure for Health Physics

Health physics begins with a scale distinction. Electron rearrangements govern ordinary chemical change and many detector signals; nuclear rearrangements govern radioactivity and nuclear reactions. Both can be initiated by ionizing radiation, but their characteristic energies differ greatly.

Learning objectives

You will identify atomic constituents, distinguish atomic and nuclear scales, connect electron binding to ionization and excitation, calculate ion charge, and explain why atomic number controls elemental identity.

Constituents and scales

An atom contains a positively charged nucleus of protons and neutrons surrounded by electrons. Proton and neutron masses are each about $1\,\mathrm{u}$; electron mass is about $5.49\times10^{-4}\,\mathrm{u}$. Nearly all atomic mass lies in the nucleus, while the electron cloud determines ordinary atomic size.

Useful approximate scales are

$$r_{\mathrm{atom}}\sim10^{-10}\,\mathrm{m}, \qquad r_{\mathrm{nucleus}}\sim10^{-15}\,\mathrm{m}.$$

The nucleus is roughly five orders of magnitude smaller in radius.

That radius comparison is more informative when converted to volume. Because volume scales as the cube of radius, the nucleus occupies only about $10^{-15}$ of the atom’s volume. The atom is not a tiny solid ball: it is a quantum system whose mass is concentrated in the nucleus and whose spatial extent is set chiefly by electron probability distributions.

The scale separation also suggests which interactions are likely. An energy transfer comparable to an electron binding energy can excite or ionize an atom without altering its nucleus. A nuclear transformation requires access to a different set of states and is not simply an especially energetic chemical reaction.

Identity and charge

Atomic number $Z$ is proton count and identifies the element. If an atom has $N_e$ electrons, its net charge is

$$q=(Z-N_e)e,$$

where $e=1.602\times10^{-19}\,\mathrm{C}$. Changing electron count forms an ion; changing proton count changes the element.

Excitation and ionization

Excitation raises an electron to a higher bound state. Ionization removes it into an unbound state. Energy conservation requires

$$E_{\mathrm{incident}} =E_{\mathrm{binding}}+K_{\mathrm{released}}+E_{\mathrm{other}}.$$

Atomic binding energies are commonly expressed in electronvolts. Nuclear transitions typically involve much larger kiloelectronvolt or megaelectronvolt scales, though ranges overlap in detail.

The example also states an approximation: recoil and other excitations are neglected. If either occurs, some of the $23.0\,\mathrm{eV}$ remainder must be assigned to it. A correct energy ledger names every retained term and explicitly identifies every omitted term.

Interpreting atomic energy scales

One electronvolt is the energy transferred when a particle with elementary charge moves through a potential difference of one volt:

$$1\,\mathrm{eV}=1.602\times10^{-19}\,\mathrm{J}.$$

Electronvolts are units of energy, not voltage and not particle type. A $20\,\mathrm{keV}$ photon and a $20\,\mathrm{keV}$ electron have equal total energy magnitudes but interact differently because their charge, mass, and interaction mechanisms differ.

Why this matters in radiation protection

Ion pairs underlie gas-filled detector signals. Excited states can yield scintillation light. Electron binding influences photon absorption, characteristic x rays, and Auger electrons. Nuclear composition, developed next, determines which atoms are radioactive.

Common mistakes

• Treating an ion as a different isotope.
• Treating electron orbits as classical planetary paths.
• Confusing ionizing radiation with radioactive material.
• Assuming all radiation interactions occur in the nucleus.

Test Your Knowledge

1. An atom has $Z=13$ and $10$ electrons. Find its charge.
2. Which change alters elemental identity: removing an electron or adding a proton?
3. Distinguish excitation from ionization.
4. An interaction deposits $50.0\,\mathrm{eV}$ and uses $15.0\,\mathrm{eV}$ to ionize an atom. Under a two-term model, how much kinetic energy remains?
5. A nucleus is unchanged but an atom emits characteristic x rays. Which part of the atom rearranged?

Solutions

1. $q=+3e=+4.81\times10^{-19}\,\mathrm{C}$.
2. Adding a proton changes $Z$ and therefore the element.
3. Excitation remains bound; ionization removes an electron from the atom.
4. $50.0\,\mathrm{eV}-15.0\,\mathrm{eV}=35.0\,\mathrm{eV}$.
5. The electron structure rearranged. An electron vacancy was filled; this does not require the nucleus to change identity.

Connection forward

Nuclide notation adds neutron number and nuclear state to the atomic-number bookkeeping used here.

Sources

• NIST Reference on Constants, Units, and Uncertainty for the elementary charge and atomic mass constant.
• U.S. Nuclear Regulatory Commission: Radiation Basics for introductory distinctions among atoms, ionization, and ionizing radiation.