MCAT Physics and Math Review

Chapter 9: Atomic and Nuclear Phenomena

Conclusion

Congratulations! You’ve finished the physics content material that will be needed for Test Day. Our last topic was the interaction of energy and matter on the atomic level. We began by examining radiant energy from matter and related temperature, wavelength, and certain constants. Next we studied the photoelectric effect. Further, we took a look at Bohr’s model of the hydrogen ion, and made some generalizations about electronic structure and the permissible states in regards to absorption and emission of light energy. We also noted that on a molecular level, small changes in structure can lead to significant shifts in absorption. We studied the interactions of the nucleus with energy including the prototypical nuclear reactions of fusion and fission. We finished our discussion of nuclear reactions by examining the most common forms of nuclear decay and some of the mathematics for determining half-life or sample remaining. In the next few chapters, we’ll focus on building Test Day skills, including MCAT math shortcuts that will make many of these concepts more rewarding.

Concept Summary

The Photoelectric Effect

·        The photoelectric effect is the ejection of an electron from the surface of a metal in response to light.

·        The threshold frequency is the minimum light frequency necessary to eject an electron from a given metal.

o   The work function is the minimum energy necessary to eject an electron from a given metal. Its value depends on the metal used and can be calculated by multiplying the threshold frequency by Planck’s constant.

o   The greater the energy of the incident photon above the work function, the more kinetic energy the ejected electron can possess.

·        The ejected electrons create a current; the magnitude of this current is proportional to the intensity of the incident beam of light.

Absorption and Emission of Light

·        The Bohr model of the atom states that electron energy levels are stable and discrete, corresponding to specific orbits.

o   An electron can jump from a lower-energy to a higher-energy orbit by absorbing a photon of light of the same frequency as the energy difference between the orbits.

o   When an electron falls from a higher-energy to a lower-energy orbit, it emits a photon of light of the same frequency as the energy difference between the orbits.

·        Absorption spectra may be impacted by small changes in molecular structure.

·        Fluorescence occurs when a species absorbs high-frequency light and then returns to its ground state in multiple steps. Each step has less energy than the absorbed light and is within the visible range of the electromagnetic spectrum.

Nuclear Binding Energy and Mass Defect

·        Nuclear binding energy is the amount of energy that is released when nucleons (protons and neutrons) bind together.

o   The more binding energy per nucleon released, the more stable the nucleus.

o   The four fundamental forces of nature are the strong and weak nuclear force, which contribute to the stability of the nucleus, electrostatic forces, and gravitation.

·        The mass defect is the difference between the mass of the unbound nucleons and the mass of the bound nucleons within the nucleus.

o   The unbound constituents have more energy and, therefore, more mass than the bound constituents.

o   The mass defect is the amount of mass converted to energy during nuclear fusion.

Nuclear Reactions

·        Fusion occurs when small nuclei combine into larger nuclei.

·        Fission occurs when a large nucleus splits into smaller nuclei.

·        Energy is released in both fusion and fission because the nuclei formed in both processes are more stable than the starting nuclei.

·        Radioactive decay is the loss of small particles from the nucleus.

o   Alpha (α) decay is the emission of an alpha particle  , which is a helium nucleus.

o   Beta-negative (β) decay is the decay of a neutron into a proton, with emission of an electron (eβ) and an antineutrino (  ).

o   Beta-positive (β+) decay, also called positron emission, is the decay of a proton into a neutron, with emission of a positron (e+β+) and a neutrino (ν).

o   Gamma (γ) decay is the emission of a gamma ray, which converts a high-energy nucleus into a more stable nucleus.

o   Electron capture is the absorption of an electron from the inner shell that combines with a proton in the nucleus to form a neutron.

·        Half-life is the amount of time required for half of a sample of radioactive nuclei to decay.

·        In exponential decay, the rate at which radioactive nuclei decay is proportional to the number of nuclei that remain.

Answers to Concept Checks

·        9.1

1.    The work function describes the minimum amount of energy necessary to emit an electron. Any additional energy from a photon will be converted to excess kinetic energy during the photoelectric effect.

2.    The threshold frequency depends on the chemical composition of a material (that is, the identity of the metal).

3.    The accumulation of moving electrons creates a current during the photoelectric effect.

·        9.2

1.    The energy differences between ground-state electrons and higher-level electron orbits determine the frequencies of light a particular material absorbs (its absorption spectrum).

2.    False. Small changes, such as protonation and deprotonation, change in oxidation state or bond order, and others may cause dramatic changes in light absorption in a material.

3.    When electrons transition from a higher-energy state to a lower-energy state, they will experience photon emission.

4.    Fluorescence is a special stepwise photon emission in which an excited electron returns to the ground state through one or more intermediate excited states. Each energy transition releases a photon of light. With smaller energy transitions than the initial energy absorbed, these materials can release photons of light in the visible range.

·        9.3

1.    The strong nuclear force is one of the four primary forces and provides the adhesive force between the nucleons (protons and neutrons) within the nucleus. Mass defect is the apparent loss of mass when nucleons come together, as some of the mass is converted into energy. That energy is called the binding energy.

2.    The four fundamental forces of nature are the strong and weak nuclear forces, electrostatic forces, and gravitation.

3.    Mass defect is related to the binding energy such that there is a transformation of nuclear matter to energy with a resultant loss of matter. They are related by the equation E = mc2.

·        9.4

1.    True. While they may seem like inverses of each other, both nuclear fusion and nuclear fission reactions release energy.

2.     

Nuclear Reaction

Size of Reactant Particles

Change in Nuclear Mass during Reaction (Increase or Decrease)

Fission

Large (actinides, lanthanides)

Decrease

Fusion

Small (hydrogen, helium)

Increase

3.     

Nuclear Reaction

Emits…

ΔZ

ΔA

Alpha decay

Alpha particle 

−2

−4

Beta-negative decay

Electron (eβ) and antineutrino (  )

+1

0

Beta-positive decay

Positron (e+, β+) and neutrino (ν).

−1

0

Gamma decay

Gamma ray (γ)

0

0

Electron capture

Nothing (absorbs an electron from inner shell)

−1

0

4.    Because the amount remaining is cut in half after each half-life, the portion remaining will never quite reach zero. This is mostly a theoretical consideration; “all” of a sample is considered to have decayed after 7 to 8 half-lives.

5.    Because gamma radiation produces electromagnetic radiation (rather than nuclear fragments), it can be detected on an atomic absorption spectrum.

Equations to Remember

(9.1) Energy of a photon of lightE = hf

(9.2) Maximum kinetic energy of an electron in the photoelectric effectKmax = hf − W

(9.3) Work functionW = hfT

(9.4) Mass defect and energyE = mc2

(9.5) Nuclear decay (general form) emitted decay particle

(9.6) Alpha decay

(9.7) Beta-negative decay

(9.8) Beta-positive decay (positron emission)

(9.9) Gamma decay

(9.10) Electron capture

(9.11) Rate of nuclear decay

(9.12) Exponential decayn = n0e−λt

(9.13) Decay constant

Shared Concepts

·        General Chemistry Chapter 1

o   Atomic Structure

·        General Chemistry Chapter 2

o   The Periodic Table

·        Organic Chemistry Chapter 11

o   Spectroscopy

·        Physics and Math Chapter 1

o   Kinematics and Dynamics

·        Physics and Math Chapter 2

o   Work and Energy

·        Physics and Math Chapter 8

o   Light and Optics