Download A Z N Atomic Mass: A = Z + N Mass and Rest Energy m =

Physics
Chapter 25 Lesson 1: The Nucleus
Atoms contain electrons, protons, and neutrons. Protons and neutrons are in the center of the atom
known as the nucleus and together they are called nucleons. All of an atom’s positive charge and
most of the atoms mass is located in the nucleus. The femtometer (fm) is used when working with
units of measure related to the size of atomic components. It is also called the fermi, which is equal
to 10–15 m.
The nucleus of an atom can be specified by an atomic number (Z) and a mass number (A). These
are written next the chemical symbol.
A
mass number = the number of nucleons in the nucleus
Z
atomic number = the number of protons in the nucleus
N
neutron number = the number of neutrons in the nucleus
Atomic Mass:
A=Z+N
Example 1: How many protons does an aluminum atom have?
How many neutrons?
The number of protons in an atom is unique for each different element, so the atomic number can be
used as a way to identify it. The atomic number is listed with the chemical symbol in a periodic table
of the elements. The mass of an element is not necessarily the same for each element since the
number of neutrons can vary. Isotopes are atoms of an element that have the same atomic
number but different neutron and mass numbers.
For example, four isotopes of carbon are
The nucleus of an atom is very dense. It can be viewed as a combination of tightly
packed spheres. Each sphere is either a neutron or a proton. All nuclei have about the
same density. The mass of a nucleus can be expressed by the unified mass unit.
1 u = 1.660 559 x 10–27 kg
Protons and neutrons each have a mass of about 1 u. Electrons are much smaller with a mass of
only about 10–4 u. The mass of the nucleus can be related to what is known as rest energy.
Mass and Rest Energy
m=
mass = (
)
A common unit of measure used when working on a nuclear level is the mega electron volt, MeV. A
volt is one joule/coulomb and the charge of an electron is -1.6 x 10-19 coulombs. An electron volt is
the energy acquired by one electron being accelerated through a potential difference of one volt.
1 volt x 1.6 x 10-19 coulombs = 1.6 x 10-19 joules = 1 eV
1 MeV = 1.6 x 10-13 J
Example 2: Determine the rest energy of a proton, neutron, and an electron. The mass of each is
given below:
mp = 1.673 x 10-27 kg
mn = 1.675 x 10-27 kg
me = 9.109 x 10-31 kg
If protons repel each other, then how does the nucleus stay bound so tightly together? This happens
because the nuclear force is a much stronger force than that of the electric force caused by repulsion.
The nuclear force is sometimes called the strong force. It is the interaction that binds nucleons
together in the nucleus. The force works with dimensions on the nuclear level that are MUCH smaller
than those found on the atomic level. For example, a radius at the nuclear level is around 10-14 m
which is about 10,000 times smaller than the radius of an atom.
Neutrons stabilize the nucleus of atoms. Light nuclei are stable when they contain about the same
amounts of protons and neutrons. Heavy nuclei are only stable if they have more neutrons than
protons. The more protons there are the more neutrons there must be to provide the attractive
nuclear forces that hold everything together.
Unstable nuclei occur with elements that have more than 83 protons. For that number of protons the
repulsive force becomes powerful enough to overcome the strong nuclear force.
Energy released when nucleons bind together to form a stable nucleus is binding energy.
Ebind = E0,unbound – E0,bound
Ebind is the binding energy. E0,unbound is the rest energy of a group of particles that are not part of a
nucleus. E0,bound is the rest energy of the same group of particles when they are part of a nucleus.
Ebind = munboundc2 – mboundc2 = (munbound – mbound)c2
Binding Energy of a Nucleus
Ebind = Δmc2
binding energy = mass defect x (speed of light)2
It is often helpful to find the mass defect in terms of u. 1 u = 931.50 MeV
Δm = (Zmp + Nmn) – (atomic mass – Zme)
Δm = (Zmp + Zme) + Nmn – atomic mass
One electron and one proton form a hydrogen atom, so the formula can be rewritten as follows:
Δm = Z(atomic mass of H) + Nmn – atomic mass
where the atomic mass of H = 1.007 825 u
Example 3: Find the binding energy per nucleon of
given that Ebind = 492.4 MeV.
Example 4: Calculate the binding energy of the following. Refer to the Table of Isotopes in
Appendix F for the atomic mass of each.
a. tritium (1 proton, 2 neutrons)
b. helium (2 protons, 2 neutrons)
c. carbon-12 (6 protons, 6 neutrons)
d. carbon-14 (6 protons, 8 neutrons)
Homework: Read pages 896 to 902 & complete Practice 25A and the Section Review on page 902