# 3. Nuclear Masses Flashcards

Z

- proton number / atomic number

- determines the place of an element in the periodic table

N

-neutron number

A

-mass number or nucleon number

A = Z + N

Nuclide

Definition

-a specific set of numbers Z, N, A determines a nuclide

Isobar

Definition

-nuclides with the same mass number, A, are isobars

Isotope

Definition

-nuclides with the same proton/atomic number, Z, are isotopes

Isotone

Definition

-nuclides with the same neutron number, N, are isotones

Why is this formula for nuclear mass incorrect?

M = Z*mp + N*mn

-due to the strong force, we cannot simply calculate the nuclear mass in this way as the binding energy makes a large contribution

Nuclide Map

- a plot of neutron number N on the x axis and proton number Z on the y axis
- there is a line that is most stable and a region of lower stability but where nuclides can still exist, this is known as the valley of stability
- outside of this nuclides are so unstable that they cannot exist
- to decay a nuclide needs to transition to one of slightly lower mass close to it on the nuclide map
- i.e. if a nuclide is surrounded by higher mass nuclides on the map then it won’t decay

Binding Energy

Definition

-the energy required to release a nucleon from the nucleus

Eb = ∫ F ds

-where the integral is taken from the nuclear radius r to infinity

Nuclear Mass

Equation

M = Z*mp + N*mn - Eb/c²

Binding Energy vs Ionisation Energy

- Eb accounts for around 1% of the nuclear mass
- comparing with the analogous electron ionisation energy:
- electron ionisation energy accounts for only ~10^(-9)% of the atomic mass
- it is clear that binding energy contributes a much more significant percentage and whilst we may be able to omit ionisation energy from atomic mass calculations, we must account for binding energy in nuclear mass calculations

Mass Defect

m = Eb / c²

Finding Binding Energy Experimentally

- found by measuring nuclear mass
- atomic masses may be measured by deflecting ions in electric and magnetic fields
- an ion in such a field follows a curved path with a particular radius of curvature
- |E gives re which is related to kinetic energy and |V give rmag which is related to momentum, from these we can determine mass

Mass Spectrometry

- particles pass through electric and magnetic fields on a curved path
- the radius of curvature is determined by energy for the electric field and momentum for the magnetic field
- the fields are tuned so that only particles of a particular mass will reach the detector