6강. 오비탈 전자배치 규칙②⎥파울리 배타 원리⎥전자의 스핀⎥훈트 규칙✍🏻 – Transcript

00:01The second rule for electron configuration in orbitals is the poly-exclusion principle discovered by the physicist Wolfgang Pauli. The poly-exclusion principle states that electrons filling the same orbital must have opposite spins. Spin refers to rotation and electrons have the property of rotating in a magnetic field with two possible spin states depending on the direction of rotation.

00:24For example, a helium atom has two electrons filling its 1s orbital. When an external magnetic field is applied, the electrons rotate within it and the two electrons in the same orbital rotate in opposite directions.

00:39When an electron rotates, it creates a magnetic field around it like a bar magnet and opposite rotation directions create opposite magnetic fields. Since electrons have two spin states when hydrogen atoms, each with one electron are passed through a magnetic field, half deflect toward the north pole and half toward the south pole.

01:03This means that even for identical hydrogen atoms, magnetic fields form in different directions around the atom, which is because the electron possesses the property of rotation. For reference, in the eighth grade you learned about the direction of the magnetic field formed when a current flows through Ampere's law.

01:23The direction of the magnetic field formed by current is opposite to that formed by the rotation of an electron. This is because the direction of the current and the direction of electron movement are opposite to each other. It is not necessary to know the specific direction of the magnetic field for each spin here.

01:42It is enough to understand that different rotation directions create different magnetic fields. There are two ways to represent two electrons with different spin directions filling a single orbital. Depending on the direction of the electrons spin, an electron rotating counterclockwise is called spin up and one rotating clockwise is called spin down.

02:06The direction is the same as the direction your thumb points when you curl your right hand in the direction of the electrons rotation. Spin up and spin down electrons rotate in opposite directions and create magnetic fields in opposite directions. Magnetic fields in opposite directions have an attractive property which is called magnetic attraction A.

02:26When electrons in the same orbital have opposite spins, they can become more stable due to this magnetic attraction. However, if electrons in the same orbital are both spin up or both spin down, they create magnetic fields in the same direction leading to repulsion and greater instability.

02:46Therefore, when electrons fill the same orbital, they exist in a stable state with opposite spins. Two electrons in the same orbital can be represented by quantum numbers, up spin, as plus one-half and down spin, as negative one-half and the quantum number indicating an electron spin state is called the spin magnetic quantum number.

03:08Last time we learned about the principle as immutable and magnetic quantum numbers to describe electrons in orbitals and with the spin magnetic quantum number, a total of four quantum numbers define an electron state. For example, an electron with up spin in a 1s orbital has a principal quantum number of one and as immutable quantum number of zero, a magnetic quantum number of zero, and a spin magnetic quantum number of plus one-half, half.

03:35Conversely, we can also interpret the state of an electron using its quantum numbers. For instance, an electron with a principal quantum number of one, as immutable quantum number of zero, magnetic quantum number of zero, and spin magnetic quantum number of negative one-half can be interpreted as an electron in the 1s orbital with a down spin.

03:55Thus, electrons filling the same orbital must have the same principal as immutable and magnetic quantum numbers, but their spin magnetic quantum numbers must be different. This is equivalent to saying that no two electrons in the same atom can have the exact same set of all four quantum numbers.

04:12Let's apply the poly-exclusion principle to represent electron configurations. First, a hydrogen atom with one electron. Has that electron filling the 1s orbital, which has the lowest energy level? When representing electron configurations in orbitals, we use a square box to denote the orbital and indicate the electron spin inside it.

04:31When an orbital is filled with only one electron, it could be an up spin or a down spin, but generally, we write the up spin electron first. The filling of an electron in a 1s orbital is represented as one secrete. Next, since a helium atom has two electrons, it can be represented with two electrons filling the 1s orbital, denoted as one square-ish.

04:54At this time, it is important to note that when two electrons fill the same orbital, they cannot have the same spin state. A lithium atom with three electrons has two electrons filling the 1s orbital, followed by one electron filling the 2s orbital, which has a higher energy level.

05:13This is represented as one square-fin cussence. Finally, a beryllium atom with four electrons has two electrons in the 1s orbital and two in the 2s orbital with the electrons in the same orbital having opposite spins.

05:30This is represented as one square-fin 2s intuos. The final rule applied to electron configurations in orbitals is Hund's rule. Hund's rule, discovered by the German physicist Friedrich Hund, states that when electrons fill orbitals of the same energy level, the state, with the greatest number of unpaired electrons is the most stable.

05:49For example, a boron atom with five electrons has two in the 1s orbital, two in the 2s orbital and one in the higher, energy 2p orbital, which can be expressed as one square-fin square-fin, two square-fin, two p-s-quam p-on.

06:08In this case, the p-orbitals consist of three orbitals with the same shape but different orientations, and these three p-orbitals are equal in energy level. Hund's rule is applied when two or more electrons occupy orbitals with equivalent energy levels such as the three p-orbitals.

06:25For example, a carbon atom with six electrons has two in the 1s orbital, two in the 2s orbital and two in the 2p orbital, which can be expressed as one s-square-fin, two square-fin, two p-square-fin.

06:40Since the three p-orbitals have the same energy level, it does not matter which orbital the electrons fill first as they're energetically equivalent. However, rather than two electrons filling a single orbital, the electrons first occupy separate orbitals as much as possible before they begin to pair up.

06:58When electrons fill an orbital, the state where two electrons with opposite spins occupy the same orbital is described as being paired and this is called an electron pair. On the other hand, an electron that occupies an orbital alone is called an unpaired electron.

07:13Since electrons carry a negative charge and there is an electrostatic repulsion between identical negative charges, it is more stable for them to exist as unpaired electrons and separate orbitals rather than being paired in a single orbital.

07:29Therefore, when electrons fill orbitals, they do so according to Hahn's rule, filling them in a way that maximizes the number of unpaired electrons first. If we look at the electron configurations of a nitrogen atom with seven electrons and an oxygen atom with eight, it is identical that two electrons fill the 1s orbital and two fill the 2s orbital.

07:50For the nitrogen atom, the three electrons each fill the 3p orbital which is expressed as one square, two square, four and square. For the oxygen atom, four electrons fill the 2p orbitals. After three electrons fill each of the 2p orbitals individually, the final electron exists in a paired state.

08:10This can be expressed as one-squiff-two, sn-2p-a-yo-viso. Just like the oxygen atom, once there are four or more electrons in the p orbitals, they must pair up so the state with three electrons in the p orbitals in nitrogen has the maximum number of unpaired electrons.

08:28Let's summarize the three rules applied when filling orbitals that we learned today. When filling in atoms' orbitals with electrons, electrons occupy the orbitals with the lowest energy levels first. To determine an orbital's energy level, a higher sum of the principal and azimuthal quantum numbers indicates a higher energy level.

08:49If the sum is the same as in 3p and 4s orbitals, the one with the higher principal quantum number has a higher energy level, representing the electron configuration of a nitrogen atom which has seven electrons. We can list the 1s, 2s and 2p orbitals in order of their energy levels.

09:09Electrons fill orbitals starting from the lowest energy level, a concept known as the Aufbau principle. Following the Aufbau principle to fill electrons in order starting from the 1s orbital, two electrons fill the 1s, two fill the 2s and three fill the 2p orbital.

09:27When two electrons occupy the same orbital, they must have opposite spins which is known as the poly exclusion principle. When filling orbitals of the same energy level, electrons occupy them singly as much as possible before pairing up a concept known as Hans rule.