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These are called nucleons. What distinguishes different elements in the periodic table is the # of protons they have in their nucleus. This is ...
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We’ve been studying atomic structure – the Rutherford model of the atom, where electrons orbit around a nucleus.
And now we know that it takes Quantum Mechanics to correctly describe the nature of these orbits.
But what about the nucleus?
Well, so far we just know about protons.
But, in 1932 scattering experiments by English physicist James Chadwick discovered another particle in the nucleus which had no charge neutron.
Shorthand notation for element representation:
16 8 The mass of the elements is usually given in atomic mass units ( u ).
1 u 1.6605 10 kg
Nuclei that contain the same number of protons but a different number of neutrons are called isotopes.
For example, boron exists in nature as two stable isotopes:
10 5
11 5 Most boron atoms have 6 neutrons (81.1%), but some (18.9%) have only 5 neutrons.
The atomic mass number (A) listed on the periodic table is the average atomic mass of the isotopes, for boron this is 10.811.
What does the nucleus look like? Why Coulomb repulsion does tear apart nucleus? The protons and neutrons are clustered together in a blob that is approximately spherical. The radius of the nucleus is ~ 1 fm = 1 × 10 -15^ m.
Experiments show that: 15 1 / 3 r ( 1. 2 10 m) A
The Nucleon Density, which is the # of protons and neutrons per unit volume, is the same for all atoms!
So we have this spherical blob of positive protons and neutral neutrons.
How does it stay together???
Example: He nucleus: 2 protons and 2 neutrons
Most nuclei listed in the periodic table are stable, but some are not.
The stability of a nucleus depends on the balancing between the electrostatic repulsion between protons and the strong nuclear attractive force between all nucleons.
Every proton in the nucleus feels Coulombic repulsion from every other proton, since the electro- static force is long-ranged.
But each proton and neutron only feels the strong nuclear force from its closest neighbors. To compensate for this, the more protons I add to the nucleus, an even greater number of neutrons must be added to try and balance the electrostatic force. As I create larger and larger nuclei, the neutron number keeps getting bigger and bigger. Notice how the neutron # deviates from the N = Z line for large nuclei.
Eventually, as more and more protons are added, no # of extra neutrons can compensate for the large electrostatic repulsion, and the nucleus breaks apart.
This occurs at Z = 83, which is bismuth (Bi).
Any element with an atomic number Z > 83 will be unstable and break apart over time. It will rearrange itself into a stable nuclei. This process is called Radioactivity.
In order to separate two nucleons, we have to overcome the strong nuclear force.
We refer to this as the Nuclear Binding Energy.
To analyze this problem quantitatively, we have to use Einstein’s famous E =mc^2.
This equation gives us the rest mass energy. Thus, a change in mass of a system equals
The binding energy of the nucleus appears as extra mass in the separated nucleons.
In other words, the sum of the masses of the individual nucleons is greater than
the nucleus.
The nuclear binding energy then is just this mass converted to energy:
2 2 Binding Energy (mass defect) c D mc
Example: The binding energy of a helium nucleus:
The most abundant isotope of helium has a nucleus whose mass is 6.6447× 10 -27^ kg. For this nucleus, calculate (a) its mass defect and (b) its binding energy.
Nucleus +
2 separated protons and 2 separated neutrons
Solution:
D m 2 mp 2 mn m Henucleus 27 27 27 2 ( 1. 6726 10 ) 2 ( 1. 6749 10 ) 6. 6447 10
D m 29 5.03 10 kg
(b)Binding Energy, E (D m ) c^2 E ( 5. 03 10 ^29 )( 3 108 )^2
So any nucleus with more than 83 protons is unstable, or radioactive. These nuclei disintegrate over time, and during this process, 3 types of radiation may be produced:
The 3 types of radiation were discovered by Becquerel in 1896, and then later labeled by Rutherford:
Increasing Energy
Alpha rays^ Beta rays Gamma rays No way to tell...
17%
3%
12%
68%
1 2
3
Clicker Question 31 - 2
U Th He 4 2
234 90
238 92
After the initial alpha decay, the daughter nucleus (^234 Th) is still radioactive. It then undergoes beta decay:
ThPa b^ Explicitly, we write this as: Th Pa e 0
234 91
234 90
Parent Nucleus (P)
Daughter Nucleus (D)
b particle (electron) So, in general then, for b decay, we have:
P D e
Z
*Notice again, that the charge is conserved!
So where does the electron come from???
It turns out that neutrons themselves are unstable, and they will decay into a proton. When the neutron decays into a proton, it releases an electron (b-) and an antineutrino (n-e)
Beta rays are negatively charged particles, and experiments show them to be electrons.
There is a 2nd^ type of b decay called b+^ decay.
Here, the nucleus emits a positron.
The positron is the electron’s antiparticle : it’s antimatter!
The positron has the same mass and spin of the electron, but opposite electric charge. The positron is created when a nuclear proton is transformed into a neutron:
P D e
Z
Parent Nucleus (P)
Daughter Nucleus (D)
b^ particle (electron)
There is a 3rd^ type of b decay called electron capture:
Here, the nucleus pulls in an orbital electron from the K-shell.
Assume I have a chunk of radioactive material that contains N radioactive nuclei, or parent nuclei. Which one of these nuclei is going to decay, and when?
Since radioactivity is a quantum-mechanical process , we can’t know with certainty. We can only predict when a particular nucleus will decay. Thus, radioactivity is a statistical process.
As time passes, some of the nuclei will decay, and N will decrease.
To help describe this process, it’s useful to define something called the half-life:
It is represented by T 1/2, and it is the time it takes for ½ of the nuclei present to decay.
So T 1/2 will have units of time [s]. If the half-life is long, it can also be represented in years.
As an example, let’s say that I have some radioactive element X which has a half- life of 1 year, and I originally start with 100 atoms of it.
How many atoms will be left after 1 year, 2 years, 3 years, and so on???
Time # of X atoms left
0 100
1 year (1 half-life) 50 (1/2 left)
2 years (2 half-lives) 25 (1/4 left)
3 years (3 half-lives) 12.5 (1/8 left)
4 years (4 half-lives) 6.25 (1/16 left)
..
n years (n half-lives) (^) n n (1/2 n^ left)
N 2 2
100
Let’s make a plot of the atoms left versus time:
