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General Chemistry - Hund's Rule and Radiation

Hund’s rule says that within any one’s subshell, electrons occupy orbital singly unless and until all of the orbitals in that subshell have one electron in them. Energy can travel. One of the modes by which energy travels is the wave of electromagnetic radiation. Its speed is 3 x 108 meters per second in a vacuum. This number, 3 x 108 meters per second, is called the speed of electromagnetic radiation and is symbolize with the letter C. You may have seen this as the speed of light. That is because visible light is a type of electromagnetic radiation.

Let us think of an electromagnetic wave as a sinusoidal wave oscillating about an axis. It is useful to describe such wave with the following measurements;
  1. A wavelength tells us the length of one full cycle of the wave. It can be measured in nanometers per cycle.
  2. A frequency, F, tells the number of cycles that passes by a given point during one second. The inverse of frequency is called the period of the wave or T.
  3. An amplitude, which is the height of the wave; it can also be thought of as the maximum displacement from the axis.

Waves of electromagnetic radiation may differ in their wavelengths, frequencies, and amplitudes, but all waves of electromagnetic radiation have a velocity of 3 x 108 meters per second, symbolized with the letter C.

Rule number 1:

Wavelength times frequency equals the speed of light or λF = C.

Using this formula, you can figure out the wavelength if you know the frequency, and you can figure out the frequency if you know the wavelength. All matter has wave characteristics. This is called the de Broglie hypothesis.

Rule number 2: The de Broglie hypothesis

Wavelength equals Planck’s constant over mass times velocity or λ = H/mv.

Planck’s constant is equal to 6.63 x 10-34 joule-seconds. The De Broglie hypothesis is mostly used in electrons. That is because all electrons have the same mass but they can differ in velocity.

Some electromagnetic waves produce light. Visible light is mostly a mixture of different waves of electromagnetic radiation within the wavelength range of 390 to 700 nanometers. If all colors are present in the mixture, the result is white light.

Lights other than white contain only some wavelengths and therefore only some colors. When light is passed through a prism, its component wavelengths are separated and a spectrum of different colors appears. These different colors correspond to the wavelengths that were present in the original light.

If we pass white light through a prism, we get something called a continuous spectrum because white light is composed of all colors. Now, if we pass a light through a prism that is not white, we get a line spectrum which shows a line for each color that is contained in the light we used.

When an atom is exposed to light, some of its electrons may absorb some of the light’s energy. As an electron absorbs energy, it becomes excited and moves from its ground state to an excited state. When the light is removed, the electron falls back to its ground state and is no longer excited. As it falls, it emits some energy in the form of light. And if this light energy is not completely removed, the electron may fall down to a lesser excited state.

You should know about the quantum theory. The quantum theory states that quanta are the smallest unit of energy that can be absorbed or emitted at a particular frequency. An important concept associated with this theory is this: When we say that an electron absorbs light energy and gets excited the electron absorbs one or more quanta of energy, not a half or two thirds of a quantum but a whole number of quanta at a time. As a result, electrons exist in the atom only at certain energy levels. After absorbing a certain number of quanta of energy, the electron now has the exact amount of extra energy to jump to an available energy level or subshell.

A nucleus is held together by a force called the nuclear force, which is non-electrical force between protons and neutrons. Some nuclei are stable and some are unstable. The unstable nuclei have a tendency to break apart. This tendency to break apart is what makes some nuclei radioactive. Unstable nuclei try to become more stable by altering their content of protons and neutrons. This process is called nuclear decay. If in the process of nuclear decay, a nucleus emits small particles, then that nucleus is radioactive.

There are three kinds of radioactive decay.

Alpha decay :
An alpha particle consists of two protons and two neutrons. Alpha decay reduces atomic number by two and reduces the mass number by four.

Beta decay :
If a nucleus wants to become more stable by reducing its neutron to proton ratio, it converts a neutron to a proton. The atomic number goes up by one, but the mass number remains the same. When this occurs, a beta particle is emitted. The beta particle is identical to an electron.

Positron emission :
If a nucleus wants to become more stable by increasing its neutron to proton ratio, it converts a proton to a neutron. The atomic number goes down by one, but the mass number remains the same. When this occurs, a positron is emitted. A positron is a particle that has the same mass as an electron but carries a positive charge.

Gamma rays :
A gamma ray is electromagnetic radiation. Gamma rays are often emitted together with alpha particles, beta particles, and positrons.

Electron capture :
Some nuclei convert a proton to neutron by capturing an electron from the first electron shell of their own atom. Somehow, the capture of the electron allows the nucleus to convert a proton to neutron. Electron capture causes the atomic number to be reduced by one while the mass number remains the same.

Remember that when a radioactive particle is emitted, it is lost and we must subtract it from our original atom. In alpha decay, subtract four from mass number, subtract two from atomic number.

In beta decay no change in mass number, add one to the atomic number.

In positron emission, no change in mass number, subtract one from atomic number.

In gamma rays, no change in mass number or atomic number.

In electron capture, no change in mass number, subtract one from atomic number.

Radioactive particles have energy, and this is their order.

  1. Gamma rays, highest energy.
  2. Beta decay and positron emission, equal energy between gamma and alpha.
  3. Alpha decay, lowest energy.

Radioactive substances decay with specific half-lives. Every radioactive substance has a decay constant, and the larger the decay constant the faster the radioactive substance will decay.

Rule number 3:

  1. The half-life of a radioactive substance is the time it takes for one half of some sample of the substances to undergo radioactive decay.
  2. The amount of radioactive substances that remains after a period of decay will decrease exponentially with increasing decay time.

Nucleons are more stable when they are all put together in the nucleus than when they were broken apart as separate protons and neutrons.

Every nucleus has what is called a nuclear binding energy. Nuclear binding energy is equal to the energy that would be required to break a nucleus up into individual nucleons. Some nuclei have higher binding energies than others. A nucleus weighs less than the sum of its protons and neutrons individually. The difference is what we call the mass defect. The reduction in energy that’s achieved when a nucleus is assembled involves a loss of mass. Einstein formulated a relationship between the nuclear binding energy and the mass defect.

Rule number 4:

For any nuclear binding energy, energy equals the mass defect times the square of the speed of electromagnetic radiation, or E = MC2.