Chemistry: Nuclear Phenomena

Question 1

Binding Energy

Answer 1

Energy required to break up a given nucleus into its constituent protons and neutrons.

That energy is converted to mass via Einstein’s E = mc², resulting in a larger mass for the constituent protons and neutrons than that of the original nucleus, the difference being called mass defect.

Question 2

Nuclei

Answer 2

At the center of an atom lies its nucleus, consisting of one or more nucleons (protons and neutrons) held together with considerably more energy than the energy needed to hold electrons in orbit around the nucleus.

The radius of the nucleus is about 100k times smaller than the radius of the atom.

Question 3

Atomic Number

Answer 3

Z is always an integer and is equal to the number of protons in the nucleus.

Each element has a unique number of protons; therefore the atomic number Z identifies the element.

Z is used as a presubscript to the chemical symbol in isotopic notation.

The chemical symbols and the atomic numbers of all the elements are given in the periodic table.

Question 4

Mass Number

Answer 4

A is an integer equal to the total number of nucleons (neutrons and protons) in a nucleus.

Let N represent the number of neutrons in a nucleus. The equation relating A, N, and Z is simply A = N + Z.

In isotopic notation, A appears as a presuperscript to the chemical symbol.

Question 5

Isotope

Answer 5

The nucleus of a given element can have different numbers of neutrons, hence different mass numbers.

For a nucleus of a given element with a given number of protons (atomic number Z), the various nuclei with different numbers of neutrons are called isotopes of that element.

The term isotope is also used in a generic sense to refer to any nucleus.

The term radionuclide is another generic term used to refer to any radioactive isotope, especially those used in nuclear medicine.

Question 6

Atomic Mass & Atomic Mass Unit

Answer 6

Atomic mass is most commonly measured in unified atomic mass units (abbreviated amu or simply u).

By definition, 1 amu is exactly 1/12 the mass of the neutral carbon-12 atom (not just the nucleus–the atom includes the nucleus and all six electrons).

In terms of more familiar mass units: 1 amu = 1.66 x 10^-27 kg = 1.66 x 10^-24 g

Question 7

Atomic Weight

Answer 7

Because isotopes exist, atoms of a given element have different masses.

The atomic weight refers to a weighted average of the masses (not the weights) of an element.

The average is weighed according to the natural abundances of the various isotopic species of an element.

The atomic weight can be measured in amu.

Question 8

Radioactivity

Answer 8

All nuclei of atoms, with the exception of hydrogen, contain protons and neutrons.

When the nucleus of an atom is unstable, it may spontaneously emit particles or electromagnetic radiation otherwise known as radioactivity.

Nuclei may also “change” when nuclear transmutation occurs. This process involves the bombardment of the nucleus by electrons, neutrons, as well as other nuclei. This is a specific type of nuclear reaction.

Question 9

Nuclear Reactions

Answer 9

Elements or isotopes are changed from one to another. Reactions result in the release of absorption of large amounts of energy. Reaction rates are generally not affected by catalysts, temperature, or pressure. Protons, neutrons, or electrons can be involved.

Question 10

Chemical Reactions

Answer 10

Atoms can be rearranged by the formation or breaking of chemical bonds. Reactions generally result in the release or absorption of small amounts of energy. Reaction rates are generally affected by catalysts, temperature, or pressure. Only electrons in the affected orbital of the atom are involved in the formation and breaking of bonds.

Question 11

Nuclear Binding Energy and Mass Defect

Answer 11

Every nucleus (other than 1,1H) has a smaller mass than the combined mass of its constituent protons and neutrons. This difference is called the mass defect.

Scientists had difficulty explaining why this mass defect occurred until Einstein discovered the equivalence of matter and energy, embodied by the equation E = mc². The mass defect is a result of matter that has been converted to energy. This energy, called binding energy, holds the nucleons together in the nucleus.

Note: The binding energy per nucleon peaks at iron, which implies that iron is the most stable atom. In general, intermediate-sized nuclei are more stable than large and small nuclei.

Question 12

Nuclear Reactions & Decay

Answer 12

Nuclear reactions such as fusion, fission, and radioactive decay involve either combining or splitting the nuclei of atoms.

Since the binding energy per nucleon is greatest for intermediate-sized atoms, when small atoms combine or large atoms splits, a great # of energy is released.

Question 13

Fusion

Answer 13

Occurs when small nuclei combine into a larger nucleus.

As an example, many stars, including the sun, power themselves by fusing four hydrogen nuclei to make one helium nucleus. By this method, the sun produces 4 x 10²⁶ J every second.

Here on Earth, researchers are trying to find ways to use fusion as an alternative energy source.

Because these fusion reactions can only take place at extremely high temperatures, they are generally referred to as thermonuclear reactions.

Question 14

Fission

Answer 14

A process in which a large, heavy (mass number > 200) atom splits to form smaller nuclei and one or more neutrons.

It’s important to note that because a large nucleus is more unstable than its products, there’s the release of a large amount of energy.

Spontaneous fission rarely occurs. However, by the absorption of a low-energy neutron, fission can be induced in certain nuclei. Of special interest are those fission reactions that release more neutrons, since these other neutrons will cause other atoms to undergo fission. This in turn releases more neutrons, creating a chain reaction. Such induced fission reactions power commercial nuclear electric-generating plants.

Some radioactive nuclei may be induced to fission via more than one decay channel or decay mode. For example, a different fission reaction may occur when uranium-235 absorbs a slow neutron and then immediately splits into barium-139, krypton-94, and 3 more neutrons with no intermediate state.

Question 15

Radioactive Decay

Answer 15

Naturally occurring spontaneous decay of certain nuclei accompanied by the emission of specific particles. It could be classified as a certain type of fission.

Radioactive decay problems are of 3 general types:

1) The integer arithmetic of particle and isotopic species.
2) Radioactive half-life problems.
3) The use of exponential decay curves and decay constants.

Question 16

Isotope Decay Arithmetic and Nucleon Conservation

Answer 16

Let the letters X and Y represent nuclear isotopes, and let us further consider the three types of decay particles and how they affected the mass number and atomic number of the parent isotope A,Z X and the resulting daughter isotope A’,Z’ Y in the decay: A,Z X –> A’,Z’ Y + emitted decay particle

Question 17

Alpha Decay

Answer 17

The emission of an alpha-particle, which is a 4,2 He nucleus that consists of two protons and two neutrons.

The alpha particle is very massive (compared to beta particle) and doubly charged. Alpha particles interact with matter very easily; hence they don’t penetrate shielding (such as lead sheets) very far.

The emission of an alpha-particle means that the daughter’s atomic number Z’ will be 2 less than the parent’s atomic number and the daughter’s mass number will be 4 less than the parent’s mass number.

This can be expressed in 2 simple equations: alpha decay

Z_daughter = Z_parent - 2

A_daughter = A_parent - 4

The generic alpha decay reaction is then:

A,Z X –> Z A-4,Z-2 Y + alpha

Question 18

Beta Decay

Answer 18

Emission of a beta-particle, which is an electron given the symbol e^- or B^-.

Electrons do not reside in the nucleus but are emitted by the nucleus when a neutron in the nucleus decays into a proton and a B^- (and an antineutrino). Since an electron is singly charged and about 1836 times lighter than a proton, the beta radiation from redioactive decay is more penetrating than alpha radiation.

In some cases of induced decay, a positively charged antielectron known as a positron is emitted. The positron is given the symble e⁺ or B⁺.

B^- decay means that a neutron disappears and a proton takes its place. Hence, the parent’s mass number is unchanged, and the parent’s atomic number is increased by 1. In other words, the daughter’s A is the same as the parent’s, and the daughter’s Z is one more than the parent’s.

In positron decay, a proton (instead of a neutron as in B- decay) splits into a positron and a neutron. Therefore, a B+ decay means that the parent’s mass number is unchanged and the parent’s atomic number is decreased by 1. In other words, the daughter’s A is the same as the parent’s, and the daughter’s Z is one less than the parent’s.

B^- Decay:
Z_daughter = Z_parent + 1
A_daughter = A_parent

B⁺ Decay:
Z_daughter = Z_parent - 1
A_daughter = A_parent

The generic negative beta decay reaction: A,Z X –> A,Z+1 Y + B^-

The generic positive beta decay reaction: A,Z X –> A,Z-1 Y + B⁺

Question 19

Gamma Decay

Answer 19

The emission of Y-particles, which are high-energy photons.

They carry no charge and simply lower the energy of the emitting (parent) nucleus w/o changing the mass number or the atomic number. In other words, the daughter’s A is the same as the parent’s and the daughter’s Z is the same as the parent’s.

Y Decay:
Z_parent = Z_daughter
A_parent = A_daughter

Generic Gamma Decay Reaction: A,Z X* –> A,Z X + Y

Question 20

Electron Capture

Answer 20

Certain unstable radionuclides are capable of capturing an inner (K or L shell) electron that combines with a proton to form a neutron. The atomic number is now one less than the original, but the mass number remains the same. Electron capture is a rare process that’s perhaps best thought or as an inverse B- decay.

Question 21

Exponential Decay

Answer 21

Let n be the number of radioactive nuclei that have not yet decayed in a sample. It turns out that the rate at which the nuclei decay (Δn/Δt) is proportional to the number that remain (n).

Δn/Δt = -DCn

Where DC is the decay constant. The solution of this equation tells us how the number of radioactive nuclei changes with time.

The solution is known as exponential decay.

n = n₀e^-DCt where n₀ is the number of undecayed nuclei at time 0. (The decay constant is related to the half-life by DC = ln 2 /T_1/2 = 0.693/T_1/2.)