1.7.1: Interactions Between Atoms: A Range of Effects

The attractions and repulsions between charged particles and magnets are both manifestations of the electromagnetic force. Our model of the interactions between atoms will involve only electric forces; that is, interactions between electrically charged particles, electrons and protons. In order to understand this we need to recall from physics that when charged particles come close to each other they interact. You probably recall that “like charges repel and unlike charges attract”, and that this interaction, which is known as a Coulombic interaction, depends on the sizes and signs of the charges, and is inversely proportional to the square of the distance between them (this interaction can be modeled by the equation:

\[\underset{\text{Coulomb’s Law}} {F \propto \dfrac{q_1 \, q)2}{ r^2}} \]

where q₁ and q₂ are the charges on the particles and r is the distance between them. That is: there is a force of attraction (or repulsion if the two charges are of the same sign) that operates between any two charged particles. This mathematical description of the electromagnetic interaction is similar to the interaction due to gravity. That is, for a gravitational interaction there must be at least two particles (e.g. you and the Earth) and the force of the attraction depends on both masses, and is inversely proportional to the square of the distance between them:

\[F \propto \dfrac{m_1 \; m_2}{r^2}\]

The difference between the two forces are:

1. gravitational interactions are much weaker than electromagnetic interactions and
2. gravity is solely an attractive interaction while electromagnetic interactions can be either attractive or repulsive.

Now, let us consider how atoms interact with one another. Taken as a whole, atoms are electrically neutral, but they are composed of discrete electrically charged particles. Moreover, their electrons behave as moving objects.²¹ When averaged over time the probability of finding an electron is spread uniformly around an atom, the atom is neutral. At any one instant, however, there is a non-zero probability that the electrons are more on one side of the atom than the other. This results in momentary fluctuations in the charge density around the atom and leads to a momentary charge build up; for a instant one side of the atom is slightly positive (δ⁺) and the other side is slightly negative (δ^–). This produces what is known as an instantaneous and transient electrical dipole - that is a charge separation. As one distorted atom nears another atom it affects the second atom’s electron density distribution and leads to what is known as an “induced dipole”. So, for example, if the slightly positive end of the atom is located next to another atom, it will attract the electron(s) in the other atom. This results in an overall attraction between the atoms that varies as 1/r⁶ – where r is the distance between the atoms. Note that this is different than the attraction between fully charged species, the Coulombic attraction, which varies as 1/r². What does that mean in practical terms? Well, most importantly it means that the effects of the interaction will be felt only when the two atoms are quite close to one another.

As two atoms approach, they will be increasingly attracted to one another. But this attraction has its limit - when the atoms get close enough, the interactions between the negatively charged electrons (and positively charged nuclei) of each atom increase very rapidly, which leads to an overall repulsion,which will stop the two atoms approaching so closely.

A similar effect was in also seen in Rutherford's experiment. Recall that he accelerated positively charged alpha particles toward a sheet of gold atoms. As an alpha particle approaches a gold atom's nucleus, the positively (+2) charged alpha particle and the gold atom’s positively (+79) nucleus begin to repel each other. If no other factors were involved, the repulsive force would approach infinity as the distance between the nuclei (r) approached 0. (You should be able to explain why.) But infinite forces are not something that happens in the macroscopic, atomic, or subatomic worlds, if only because the total energy in the universe is not infinite. As the distance between the alpha particle and gold nucleus approaches zero, the repulsive interaction grows strong enough to slow the incoming alpha particle and then push it away from the target particle. If the target particle is heavy compared to the incoming particle, as it was in Rutherford's experiments, the target, composed of gold atoms that weigh about 50 times as much as the alpha particle, will not move much while the incoming alpha particle will be reflected away. But, if the target and incoming particle are of similar mass, then both will be affected by the interaction and both will move. Interestingly, if the incoming particle had enough initial energy to get close enough (within ~10^-15 m) to the target nucleus, then the strong nuclear force of attraction would come into play and start to stabilize the system. The result would be the fusion of the two nuclei and the creation of a different element, a process that occurs only in very high-energy systems such as the center of stars or during a stellar explosion, a supernova. We return to this idea in Chapter 3.

Questions to Answer

1. How does the discovery that atoms have parts alter Dalton's atomic theory?
2. What would the distribution of alpha particles, relative to the incident beam, look like if the positive nucleus took up the whole atom (sort of like the plum pudding)? What if it took up 50% of the atom?
3. What does the distribution of alpha particles actually look like (recall that 1 in every 8000 particles were deflected)?

References

²¹ Yes we did tell you to think of electrons as a cloud - because this is a helpful model - but electrons are both particles and “clouds” as we will discuss later, in fact in some instances they appear to be quite close to perfect spheres in shape, In fact “The experiment, which spanned more than a decade, suggests that the electron differs from being perfectly round by less than 0.000000000000000000000000001 cm. This means that if the electron was magnified to the size of the solar system, it would still appear spherical to within the width of a human hair. (Hudson et al "Improved measurement of the shape of the electron" DOI: 10.1038/nature10104).