Neutron Stability in Atomic Nuclei | Of Particular Significance
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In the Bohr model of an atom, electrons could be found only at certain allowed distances from the nucleus. Bohr's model was also consistent with the earlier idea of the periodic table of the elements. The idea is that electrons are found in different "shells" that are each further and further from the nucleus. Each of those shells corresponds roughly to a different row in the periodic table. Hydrogen and helium have electrons only in the first shell, and we see those two elements in the first row of the periodic table.
Carbon and oxygen's outermost electrons are found in the second shell, so they show up in the second row of the periodic table. Each row in the periodic table corresponds to an outer layer of electrons that are found further from the nucleus than the outermost electrons in the row before it. We are going to see eventually that there is a further variation on this idea, but it is still pretty much the way we see the periodic table today.
Hydrogen starts the first shell, lithium the second, sodium the Latin, natrium the third, potassium Latin, kalium the fourth, and so on. The variation we are going to see involves that dip in the middle of the periodic table.
Scandium through zinc have outer electrons that are only in the third shell, not the fourth. The third and the fourth shell overlap a little bit, so that some electrons actually start to go into the fourth shell as in potassium and calciumthen finish filling the third shell across the transition metals.
The reasons for that also have to do with quantum mechanics, but we will need to learn a little more about energy and waves before we see why. Bohr showed that electrons might be found in specific orbits around the nucleus. He also showed that electrons in these different orbits have specific amounts of energy.
The Molecular Relationship, Chapter 3
By doing this mathematically, he was offering an explanation to an important problem. People knew that atoms can absorb energy they can be heated in a flame, for example and give the energy back again in the form of light. Rather than give off light of all colours when excited, atoms only give off very specific colours. For example, heating lithium salts in a flame produces a red colour, but heating sodium salts produces an orange colour, whereas potassium salts produce a purple colour, and so on.
These colours can be separated and studied using a prism.
Protons, Neutrons, and Electrons
When people did that, they found that a given atom does not produce just one pure colour of light, but several different ones. When separated by a prism, the light given off by an excited compound could be seen against a dark surface as several different, coloured lines. These were called emission lines.
It had been known since the early 's that light had wave properties, and that light of different colours had different wavelengths. For example, red light consistes of electromagnetic waves, with a wavelength of about nm, but blue light's wavelength is about nm. That means a colour can actually be measured numerically.
Because of that fact, people can look for mathematical relationships between the emission lines observed for different atoms.
Those mathematical relationships may reveal something about the atoms themselves. Furthermore, it was known that different wavelengths of light corresponded to different amounts of energy.
In one of the first developments in quantum mechanics, Max Planck in proposed that light travels in bundles called photons. Although they are particles, these photons do have wave properties. The amount of energy in a photon of light corresponds to its wavelength.
By proposing that electrons could be found only in specific orbits, specific distances away from the nucleus, Bohr was trying to explain observations from atomic spectroscopy reported by another scientist named Rydberg.
Rydberg had found a mathematical relationship between the wavelengths of these emission lines. Bohr thought that, when energy was added, electrons could be excited from one energy level or orbit to a higher one. When the electron relaxed back to its original orbit, it gave off the energy it had gained in the form of light.
The relationship between protons and prime numbers - Groundpotential Theory
The specific emission lines occur because electrons are found at very specific energy levels in an atom, so a drop from one level to another always produces the same amount of light energy. That specific amount of light energy has a specific colour. The correspondence between colour, wavelength and energy.
Bohr then used the mathematical relationships describing electrostatic attraction and centripetal force to show that his model of the atom was consistent with Rydberg's relationship. In fact, he could use his model to predict the emission lines of an atom.
Bohr's explanation of atomic structure built on Rydberg's observation of a numerical series in spectral emission lines. Solving a series involves finding a pattern in numbers. Find the patterns among the following sequences of numbers, and predict the next number in the sequence. Bohr's idea depended partly on the use of Coulomb's Law of electrostatic attraction. Coulomb's law is expressed mathematically as follows: A large value of F means that the charges are strongly attracted to each other.
What happens to the force of attraction between an electron and the nucleus when the charge in the nucleus increases? What happens to the force of attraction between an electron and nucleus when the electron gets further from the nucleus?
Max Planck described the energy of a photon using the following relationship: Other people were familiar with these ideas and already knew about the relationship between light and energy. Bohr's model of the atoms put all of these ideas together to successfully explain a specific atomic property: In other words, an excited electron can drop back to its original orbit by giving off a photon with an energy exactly the same as the difference in energy between the two orbits "excited state" and "ground state" orbits.
An electron can be thought of as both a particle and a wave. However, Bohr did not explain why electrons would be found at specific energy levels in the first place.
Louis de Broglie, a historian-turned-physicist, solved this problem with the idea of wave-particle duality. All moving particles have wave properties. Electrons move around the nucleus and they have wavelengths.
To maintain a complete standing wave along its orbit, an electron can only adopt orbits of specific circumferences. Otherwise, one end of the wave would not meet up with the other end, and it would interfere with itself. Orbits with specific circumferences have specific radii.
Electrons are found at specific distances from the nucleus, but not at other distances. One way to illustrate why an electron might have only certain allowed orbits is via the "particle in a box", a basic concept from quantum mechanics.
If a particle has wave properties, then it has a wavelength. Its wavelength depends on certain conditions. By analogy, if you take a guitar string and attach it to the ends of a box, the string can only vibrate at certain frequencies. Where does this condition come from? It comes from energy conservation. A neutron on its own will decay after a few minutes to a proton, and electron and an anti-neutrino of electron type.
Structure of the Atom
The energy bookkeeping is shown in Figure 3. The decay is shown in Figure 2; the neutron spontaneously converts into these three particles. A neutron or proton has a measured diameter of about a billionth of a trillionth of a metertimes smaller than an atomwhile the diameter of an electron or neutrino is known to be at least times smaller than that. The mass of the neutron is measured to be 0.
And the mass-energy of the neutron is therefore 0. Well, energy is conserved, and since no energy came in from outside, the energy of the system must still be the same as before: But how is this energy distributed?! First, there is no interaction energy. Second, there is mass-energy for each of the three particles.
How much mass-energy is there? So the total mass-energy is 0. The excess energy is indicated in yellow in Figure 3. We can make up the difference, however, with motion-energy. Motion-energy is always positive. As long as we distribute the excess 0. Only the total motion-energy is always the same: