NUKE VARIABLES

Ax

average atomic mass of the element; found using Equation 1 when the element contains multiple isotopes; units are typically atomic mass units (amu)

γᵢ

atomic fraction of isotope i; tells you what fraction of the atoms are isotope i; found from the isotope abundance usually given as a percentage and converted to a decimal

Aᵢ

atomic mass of isotope i; the mass of the specific isotope; found on a chart of nuclides or from the nuclear data provided in the problem

Σᵢ

sum over all isotopes or species i; means you add the contribution from every isotope present

Ax = ∑ᵢ γᵢAᵢ

average atomic mass of an element; multiply each isotope’s atomic fraction by its atomic mass and add all of the isotope contributions together

wₓ

weight fraction of element x; represents the fraction of the total mass of a compound that comes from element x; calculated from the chemical formula using Equation 2

n

number of atoms of element x in the chemical formula; found by looking at the subscript of x in the chemical formula

Ax

atomic mass of element x; found on the periodic table

m

number of atoms of element y in the chemical formula; found by looking at the subscript of y in the chemical formula

Ay

atomic mass of element y; found on the periodic table

nAx

total mass contribution of element x in the chemical formula; multiply the number of x atoms by the atomic mass of x

mAy

total mass contribution of element y in the chemical formula; multiply the number of y atoms by the atomic mass of y

wₓ = nAx/(nAx + mAy)

weight fraction of element x in a compound; divide the mass contribution of x by the total mass of the compound

wᵢ

weight fraction of isotope i; represents the fraction of the total mass that comes from isotope i; found from the isotope abundance when the abundance is given by mass or weight

Aᵢ

atomic mass of isotope i; mass of the specific isotope; found on a chart of nuclides or in the problem

Σᵢ

sum over all isotopes; means you perform the calculation for every isotope and add the results together

Ax

average atomic mass of the element; the overall average atomic mass after accounting for the weight fractions of all isotopes

Ax = [∑ᵢ(wᵢ/Aᵢ)]⁻¹

average atomic mass from weight fractions; calculate wᵢ/Aᵢ for every isotope add the values then take the inverse of the result

Nᵢ

number density of isotope i; number of atoms of isotope i per unit volume; typically units of atoms/cm³ or atoms/m³; this is what the equation is solving for

γᵢ

atomic fraction of isotope i; fraction of all atoms that are isotope i; found from the isotope abundanceusually given as a percentage and converted to a decimal

ρₓ

mass density of the element or material; mass per unit volume; given in the problem or a reference table; typically g/cm³ or kg/m³

Nₐ

Avogadro’s number; number of particles in one mole; 6.022 × 10²³ particles/mol; a constant

Ax

average atomic mass of the element; found using Equation 1 if multiple isotopes are present; can also be provided in a problem or reference table

Nᵢ = γᵢρₓNₐ/Ax

number density of isotope i; uses the isotope’s atomic fraction, material density Avogadro’s number and average atomic mass to determine the number of atoms of that isotope per unit volume

ρᵢ

mass density of isotope i; the mass of isotope i per unit volume; typically units of g/cm³ or kg/m³; this is what the equation calculates

wᵢ

weight fraction of isotope i; fraction of the material's total mass that comes from isotope i; given in the problem or calculated from isotope information

ρₓ

total mass density of the element or material; mass per unit volume of the entire material; given in the problem or a reference table

ρᵢ = wᵢρₓ

mass density of isotope i; multiply the isotope’s weight fraction by the total material density to determine the density contributed by that isotope

Nᵢ

number density of isotope i; number of atoms of isotope i per unit volume; typically atoms/cm³ or atoms/m³; this is what the equation calculates

wᵢ

weight fraction of isotope i; fraction of the total mass belonging to isotope i; given in the problem or calculated from isotope abundance information

ρₓ

total mass density of the material; mass per unit volume; given in the problem or a reference table

Nₐ

Avogadro’s number; 6.022 × 10²³ particles/mol; a constant

Aᵢ

atomic mass of isotope i; mass of the specific isotope; found on a chart of nuclides or given in the problem

Nᵢ = wᵢρₓNₐ/Aᵢ

number density of isotope i; uses the isotope’s weight fraction, total material density, Avogadro’s number, and isotope atomic mass to calculate how many atoms of that isotope exist per unit volume,

γᵢ

atomic fraction; find from isotope abundance; convert percentage to decimal

wᵢ

weight fraction; find from mass/isotope abundance information or calculate from the material composition

Aᵢ

isotope atomic mass; find on the chart of nuclides

Ax

average atomic mass; find on the periodic table for a naturally occurring element or calculate with Equation 1/3 when isotope information is provided

ρₓ

material mass density; find in the problem statement or a reference table

Nₐ

Avogadro’s number; constant; 6.022 × 10²³ particles/mol

n

number of atoms of an element in a chemical formula; find from the chemical formula subscript

m

number of atoms of the other element in a chemical formula; find from the chemical formula subscript

Nᵢ

number density; usually the variable you are solving for; units are atoms/volume

ρᵢ

isotope mass density; usually the variable you are solving for in Equation 5; units are mass/volume

alpha decay

add a helium atom to the other side

beta decay (B minus)

add a beta particle with a minus one protron charge and also add an antineutreon

positron decay

add a beta particle as well as a antineutro. Then subtract one from the protrons of the atom

gamma decay(Y)

the nucleas is in an excited state and it transfers over to its regular state plus the funky y

neutron emission

a type of radioactive decay where an unstable atomic nucleas ejects one or more free neutrons to become more stable. Happens on the far left of the chart of the nuclides.

proton emission

in the top left boundary where a protons is ejected from the nucleus.

internal conversion

an excited atomic nucleas transfers its energy directly to an orbital electron which ejects it from the atom. Dominant in heavy nuclei in the lower right regions of the chart.

electron capture

where an unstable nucleai absorbs an innner orbital electron, converting a protron into a neutron and emmiting a neutron. Below and to the right of the parent.

what does it mean if the mass number is greater than the average atomic mass

the nucleus has too many neutrons and to become more stable with mostly undergo beta minus decay

What does it mean if the average atomic mass is greater than the mass number

this means that the isotope is nutrient deficient and will likely undergo weather positron decay or electron capture

what form of decay is likey to happen if the average atomic mass and the mass number are equal

there is no specific form for decay

what does binding energy show? What does a large binding number mean

binding energy shows how much force it takes to hold the nucleus. A large binding number means that it would require more energy to dissasoicate the nucleus making it more stable

what does a protron seperation energy versus a neutron seperation energy mean?

protron shows how much energy it takes to remove a protron from the nucleas. Vice versa for neutrons. Protrons seperation energy is usually lower than the neutron seperation in stable nuclei. This is because neutrons like to pair and to remove them from the nucleas you have to break them first.

what are the magic numbers and why do scientisits believe they indicate aytpical nuclear stability

Magic numbers are (2,8,20,28, 50, 82, and 126) since these fill a shelll of a neutron. This means that the atom is not trying to gain or lose an electron which makes it more stable. These are also more likey to be natural abundance of these atoms.

origin of the unit electron volt

it is the kinetic energy imparted to an electron accelerated through a potential difference of 1V.

exoergic

means that the Q value is greater than 0 and is therefore a release of energy.

endoergic

the Q value is negative meaning that the reaction absorbs energy from its surroundings.

Atomic structure,

Atomic structure

An atom consists of a small

Typical size of an atom

About \(10^{-10}\) m (0

1 nm)

Typical size of a nucleus

About \(10^{-15}\) m (1 fm)

Nuclear mass percentage

The nucleus contains approximately 99.9% of an atom's total mass

Electron cloud space percentage

The electron cloud occupies approximately 99.999999999% of the atom's volume

Proton-to-electron mass ratio

Approximately 1836:1; a proton is about 1836 times more massive than an electron

Neutron-to-proton mass ratio

Approximately 1.0014:1; the neutron is slightly more massive than the proton

Nuclide

A specific nucleus characterized by its number of protons \(Z\) and number of neutrons \(N\)

Isotope

Nuclides of the same element that have the same number of protons \(Z\) but different numbers of neutrons \(N\)

Atomic number \(Z\)

Number of protons in the nucleus; determines the element

Mass number \(A\)

Total number of protons and neutrons; \(A=Z+N\)

Number of neutrons \(N\)

N=A-Z

Standard nuclide notation

A, Z [ X] where x is the elemental symbol, A is the mass number, and Z is the atomic number

Chart of Nuclides

A chart that organizes nuclides according to their number of protons \(Z\) and neutrons \(N\) showing information such as stability, radioactive decay, half-life, and decay modes

Natural abundance

The percentage of an element found in nature that consists of a particular isotope

Elemental molar mass

The weighted-average molar mass of an element based on the natural abundances of its isotopes

Weighted-average elemental molar mass

M=[sum] fiMi wher fi is the fractional abundance and Mi is the isotopes mass

Atomic mass unit (amu)

A unit of mass defined as \(1/12\) the mass of a neutral carbon-12 atom; 1 amu= 1.66054×10^-27 kg

MeV

Mega-electron volt; I MeV =10^6 eV common unit of nuclear energy

Electron volt (eV)

The energy gained by a particle with one elementary charge when accelerated through a potential difference of 1 volt

Mass-energy equivalence

Einstein's equation \(E=mc^2\)

Mass-energy equivalence in nuclear units

1 amu c² = 931.5 MeV

Number density

The number of atoms, nucleai, or particles per unit volume, N/V, typically in atoms/cm³ or atoms/m³

Number density of a pure element

N=pNa/M p is density, Na is avogradros numbers, and M is molar mass

Number density of an isotope

Ni = pNa/ M fi where fi is the isotopes fractional abundance.

Avogadro's number

Na= 6.022 ×10²³ particles/mole

Relativity

Time dilation

A moving clock is measured to run slower relative to a stationary observer; delta t= gamma change in time not

Lorentz factor

gamma= 1/root(1-v²/c²)

Length contraction

An object's measured length in the direction of motion decreases as its speed approaches L= Lnot/ lorenz factor

Relativistic mass increase

In the traditional formulation relativistic mass increases with velocity according to m=γm0 Modern physics generally uses invariant/rest mass m0m_0 and treats the additional energy as relativistic energy rather than an increase in rest mass.

Speed of light

c=3.0 × 10^8 m/s

Relativistic kinetic energy

KE = (gamma -1)m0c²

What happens to kinetic energy as velocity approaches \(c\)?

The kinetic energy increases enormously and approaches infinity as v→c this manifests as an increase in relativistic energy/momentum

Liquid Drop Model

A model that treats the nucleus somewhat like a drop of incompressible nuclear fluid and explains nuclear binding energy using competing effects

Five Liquid Drop Model terms

Volume surface, Coulomb, asymmetry, and pairing terms.

Volume term

Each nucleon interacts with nearby nucleons providing an attractive contribution to binding energy; larger nuclei gain more binding from this effect.

Surface term

Nucleons at the surface have fewer neighboring nucleons, reducing their binding compared with nucleons inside the nucleus.