what two kinds of rotational motion do electrons in an atom appear to have

General Rules for Assigning Electrons to Atomic Orbitals

An atom'southward electrons exist in discrete atomic orbitals, and the atom's electron configuration can be determined using a set of guidelines.

Learning Objectives

Determine the electron configuration for elements and ions, identifying the relation betwixt electron shells and subshells.

Cardinal Takeaways

Key Points

• If the energy of an cantlet is increased, an electron in the cantlet gets excited. To become back to its footing state, the electron releases energy. The free energy of the low-cal released when an electron drops in energy level is the same as the difference in energy between the two levels.
• Viewed just, electrons are arranged in shells around an cantlet'due south nucleus. Electrons closest to the nucleus will have the lowest free energy. Electrons further away from the nucleus will have higher energy. An atom's electron shell can accommodate 2n² electrons (where n is the crush level).
• In a more realistic model, electrons move in diminutive orbitals, or subshells. In that location are 4 different orbital shapes: s, p, d, and f. Within each shell, the s subshell is at a lower energy than the p. An orbital diagram is used to determine an atom's electron configuration.
• There are guidelines for determining the electron configuration of an atom. An electron will move to the orbital with lowest energy. Each orbital can hold merely i electron pair. Electrons will carve up as much as possible within a shell.

Fundamental Terms

• frequency: The number of occurrences of a repeating event per unit of time.
• quantization: The process of approximating a continuous betoken by a set of discrete symbols or integer values.

Free energy of Electrons in Diminutive Orbitals

The central structure of an atom is the nucleus, which contains protons and neutrons. This nucleus is surrounded past electrons. Although these electrons all accept the same charge and the same mass, each electron in an atom has a different amount of energy. Electrons with the lowest energy are found closest to the nucleus, where the attractive force of the positively charged nucleus is the greatest. Electrons that have higher free energy are plant further away.

Energy Quantization

When the free energy of an atom is increased (for example, when a substance is heated), the energy of the electrons inside the cantlet is as well increased—that is to say, the electrons go excited. For the excited electron to go back to its original free energy, or ground state, information technology needs to release energy. One way an electron tin can release energy is by emitting light. Each element emits light at a specific frequency (or colour) upon heating that corresponds to the energy of the electronic excitation.

It is helpful to think of this similar going up a flight of steps. If you don't lift your foot plenty, y'all volition bump into the step and be stuck on the footing level. You need to elevator your foot to the meridian of the step to movement on. The aforementioned goes for electrons and the amount of free energy they tin have. This separating of electrons into energy units is chosen quantization of energy because at that place are only certain quantities of free energy that an electron can have in an cantlet. The energy of the calorie-free released when an electron drops down from a higher energy level to a lower energy level is the aforementioned as the difference in energy between the two levels.

Electron Shells

We will showtime with a very simple mode of showing the system of electrons around an cantlet. Here, electrons are arranged in energy levels, or shells, around the nucleus of an atom. Electrons that are in the offset energy level (energy level i) are closest to the nucleus and volition have the everyman energy. Electrons further abroad from the nucleus will have higher energy. An atom's electron shell can accommodate 2n² electrons, where n is the energy level. For example, the first shell can conform two 10 (one)² or 2 electrons. The 2nd shell tin can accommodate 2 x (2)², or 8, electrons.

The arrangement of electrons in a lithium cantlet: Lithium (Li) has an diminutive number of 3, significant that in a neutral atom, the number of electrons will exist iii. The energy levels are shown every bit concentric circles around the central nucleus, and the electrons are placed from the inside out. The commencement two electrons are institute in the beginning energy level, and the third electron is found in the second energy level.

As an example, fluorine (F), has an atomic number of nine, meaning that a neutral fluorine atom has 9 electrons. The first 2 electrons are found in the start energy level, and the other seven are found in the 2nd energy level.

Atomic Orbitals

Though electrons tin exist represented simply as circumvoluted the nucleus in rings, in reality, electrons movement along paths that are much more than complicated. These paths are called diminutive orbitals, or subshells. There are several different orbital shapes—s, p, d, and f—simply nosotros will be focusing mainly on s and p orbitals for now. The first energy level contains only one s orbital, the second energy level contains i s orbital and 3 p orbitals, and the third free energy level contains one s orbital, three p orbitals, and v d orbitals. Within each energy level, the s orbital is at a lower energy than the p orbitals.

Orbital diagram: The positions of the first ten orbits of an atom on an free energy diagram. Notation that each cake is able to concord two electrons.

An orbital diagram helps to determine the electron configuration of an chemical element. An chemical element'southward electron configuration is the arrangement of the electrons in the shells. There are a few guidelines for working out this configuration:

• Each orbital can concur merely two electrons. Electrons that occur together in an orbital are called an electron pair.
• An electron will e'er try to enter the orbital with the lowest energy.
• An electron tin occupy an orbital on its own, but it would rather occupy a lower-energy orbital with another electron before occupying a higher-energy orbital. In other words, within one energy level, electrons volition fill an s orbital earlier starting to fill p orbitals.
• The due south subshell can concord 2 electrons.
• The p subshells can hold 6 electrons.

Electron configurations tin be used to rationalize chemic backdrop in both inorganic and organic chemistry. It is also used to interpret diminutive spectra, the method used to measure the energy of lite emitted from elements and compounds.

The Building-Upwards (Aufbau) Principle

The Aufbau principle determines an atom's electron configuration past adding electrons to diminutive orbitals following a defined prepare of rules.

Learning Objectives

Write electron configurations for elements in standard notation.

Fundamental Takeaways

Key Points

• The Madelung rule defines the guild in which diminutive orbitals are filled with electrons. Electrons fill orbitals starting at the lowest available energy country earlier filling higher states.
• Aufbau procedure: Determine number of electrons for the atom of involvement. Fill available orbitals starting with the lowest-energy levels starting time and avert pairing electrons in a single orbital until information technology is necessary.
• Electron configuration note describes the free energy levels, orbitals, and the number of electron. The number and letter describe the energy level and orbital respectively, and the superscript number shows how many electrons are in that orbital.
• The Aufbau principle works well for the get-go 18 elements just then becomes less useful.

Key Terms

• Pauli Exclusion Principle: The quantum mechanical principle that no 2 identical fermions (particles with one-half-integer spin) may occupy the same quantum state simultaneously.

Atoms Are Built Upwardly by Adding Electrons

Although the nucleus of an atom is very dense, the electrons around information technology can take on a variety of positions which tin can be summarized as an electron configuration. An element's electron configuration can exist represented using free energy level diagrams, or Aufbau diagrams. The Aufbau principle (from the German Aufbau meaning "building up, structure") describes a model-building method in which an atom is "built up" by progressively adding electrons. As electrons are added, they assume the nigh stable shells with respect to the nucleus and the electrons already present.

Filling in an Aufbau Diagram

The order in which orbitals are filled is given by the Madelung rule. The rule is based on the full number of nodes in the atomic orbital, n + ℓ, which is related to the energy. In this context, n represents the principal quantum number and ℓ represents the azimuthal breakthrough number. The values ℓ = 0, ane, 2, 3 correspond to the s, p, d, and f labels, respectively. According to the principle, electrons fill up orbitals starting at the everyman available energy states before filling higher states (e.k., 1s before 2s).

The Madelung free energy ordering rule: Order in which orbitals are bundled by increasing energy co-ordinate to the Madelung Dominion. Each diagonal read arrow corresponds to a unlike value of north + l.

An Aufbau diagram uses arrows to stand for electrons. When there are two electrons in an orbital, the electrons are called an electron pair. Electron pairs are shown with arrows pointing in reverse directions. According to the Pauli Exclusion Principle, ii electrons in an orbital will not spin the same way. That is, an Aufbau diagram uses arrows pointing in opposite directions. An arrow pointing upward denotes an electron spinning one way and an arrow pointing downwards denotes an electron spinning the other mode. If the orbital only has i electron, this electron is called an unpaired electron.

Aufbau diagram for lithium: The electron configuration of lithium, shown on an Aufbau diagram

The following steps detail how to draw an Aufbau diagram:

1. Determine the number of electrons that the atom has.
2. Fill the s orbital in the get-go energy level (the 1s orbital) with the first two electrons.
3. Fill the s orbital in the second energy level (the 2s orbital) with the second ii electrons.
4. Put one electron in each of the three p orbitals in the 2d energy level (the 2p orbitals) and so if at that place are nevertheless electrons remaining, go dorsum and place a second electron in each of the 2p orbitals to complete the electron pairs.
5. Continue in this style through each of the successive energy levels until all the electrons accept been drawn.

Aufbau diagram for fluorine: An Aufbau diagram showing the electron configuration of fluorine.

Electron Configuration Standard Note

A special type of notation is used to write an atom'due south electron configuration. The notation describes the energy levels, orbitals, and the number of electrons in each. For example, the electron configuration of lithium is 1sⁱⁱ2sⁱ. The number and letter of the alphabet describe the energy level and orbital, and the number above the orbital shows how many electrons are in that orbital. Using standard note, the electron configuration of fluorine is 1s^two2s^two2p^v.

Limitations to Aufbau

The Aufbau principle is based on the idea that the order of orbital energies is fixed—both for a given element and between different elements. This supposition is approximately truthful—enough for the principle to be useful—but not physically reasonable. It models diminutive orbitals every bit "boxes" of fixed free energy into which at most 2 electrons can be placed. All the same, the energy of an electron in an diminutive orbital depends on the energies of all the other electrons of the atom.

In a hydrogen-like cantlet, which only has one electron, the s-orbital and the p-orbitals of the same beat in the Aufbau diagram have exactly the same free energy. However, in a real hydrogen atom, the free energy levels are slightly split past the magnetic field of the nucleus. Because each atom has a different number of protons in its nucleus, the magnetic field differs, which alters the pull on each electron. In general, the Aufbau principle works very well for the ground states of the atoms for the beginning 18 elements, and so decreasingly well for the following 100 elements.

Interactive: Energy Levels of a Hydrogen Atom: The likely location of an electron around the nucleus of an atom is called an orbital. The shape of an orbital depends on the energy state of the electron. A neutral hydrogen atom has one electron. Click in the boxes to fix the energy of that electron and see the orbital shape describing where you are likely to find that electron around the nucleus.

Hund's Rule

Hund's Rule defines the behavior of unpaired valence shell electrons, providing insight into an atom'southward reactivity and stability.

Learning Objectives

Use Hund's dominion and justify its use to determine electron configurations for atoms in the footing land

Key Takeaways

Key Points

• Hund's Dominion states that every orbital in a sublevel is singly occupied before whatsoever orbital is doubly occupied and all of the electrons in singly occupied orbitals have the same spin.
• Electrons arrange themselves in order to minimize their interaction energy. They will always occupy an empty orbital before they pair upward to minimize repulsion. Unpaired electrons accept the aforementioned spins because they come across less often if traveling in the same direction than if traveling in contrary directions.
• To avert confusion, scientists always draw the first electron, and whatsoever other unpaired electron, in an orbital every bit "spin-upwards."
• Electron configurations assist make predictions about how certain elements volition react. An cantlet is most reactive when its valence shell is not full and about stable when its valence orbitals are total. Elements that take the aforementioned number of valence electrons often have similar backdrop.

Key Terms

• repulsion: A strength that moves two bodies abroad from each other.
• hund's dominion: A rule which states that a greater total spin country usually makes the resulting atom more stable.
• breakthrough-mechanical calculation: Branch of physics which studies matter and energy at the level of atoms and other simple particles, and substitutes probabilistic mechanisms for classical Newtonian ones.

Relation to Aufbau Principle

Electrons will fill the lowest energy orbitals first and then move up to college energy orbitals only later on the lower free energy orbitals are total. This is referred to as the Aufbau Principle, after the scientist who proposed the concept. Although the implications are articulate for orbitals of dissimilar principal breakthrough number (n), which are clearly of different energy, the filling social club is less clear for degenerate sublevels. For instance, for boron through neon, the electron filling order of the 2p orbitals follows Hund's Rule.

Hund's Dominion states that:

1. Every orbital in a sublevel is singly occupied before any orbital is doubly occupied.
2. All of the electrons in singly occupied orbitals have the same spin.

Hund's Rule Explained

According to the first rule, electrons will e'er occupy an empty orbital before they pair up. Electrons are negatively charged and, as a consequence, they repel each other. Electrons tend to minimize repulsion by occupying their own orbital, rather than sharing an orbital with another electron. Further, quantum-mechanical calculations have shown that the electrons in singly occupied orbitals are less finer screened or shielded from the nucleus.

For the 2nd rule, unpaired electrons in singly occupied orbitals have the aforementioned spins. If all electrons are orbiting in the same direction, they run into less oftentimes than if some of them orbit in opposite directions. In the latter case, the repulsive force increases, which separates electrons. Therefore, spins that are aligned have lower free energy.

Technically speaking, the first electron in a sublevel could exist either "spin-upwardly" or "spin-downwardly." Once the spin of the beginning electron in a sublevel is chosen, the spins of all of the other electrons in that sublevel depend on that first pick. To avert defoliation, scientists ever draw the first electron, and any other unpaired electron, in an orbital equally "spin-upwards."

Applying Hund's Rule

For instance, have the electron configuration for carbon: 2 electrons will pair upward in the 1s orbital, two electrons pair up in the 2s orbital, and the remaining ii electrons will be placed into the 2p orbitals. The correct orbital diagram, obeying Hund's Dominion, volition note the two 2p electrons to exist unpaired in 2 of the iii available orbitals, both with "spin-upward." Since electrons e'er occupy an empty orbital before they fill up upwards, information technology would be incorrect to describe the two 2p electrons in the same orbital, leaving open orbitals unfilled.

Instance of Hund's dominion: Orbital diagram for carbon, showing the correct application of Hund's Rule.

Equally another example, oxygen has eight electrons. The electron configuration tin can be written as 1sⁱⁱ2s^two2p⁴. The orbital diagram is drawn equally follows: the outset 2 electrons volition pair up in the 1s orbital; the next 2 electrons will pair up in the 2s orbital. That leaves 4 electrons, which must be placed in the 2p orbitals. According to Hund's Dominion, all orbitals will be singly occupied before any is doubly occupied. Therefore, 2 p orbitals will each get i electron and ane will get 2 electrons. Hund'southward Rule also tells us that all of the unpaired electrons must take the same spin. Keeping with convention, all of the unpaired electrons are fatigued equally "spin-up."

Application of Hund's rule: Orbital diagram for oxygen, which has four 2p electrons, showing the correct awarding of Hund'south Rule.

Purpose of Electron Configurations

When atoms come into contact with one another, it is the outermost electrons of these atoms, or valence shell, that will interact get-go. An atom is least stable (and therefore most reactive) when its valence shell is not full. The valence electrons are largely responsible for an element'due south chemical behavior. Elements that have the aforementioned number of valence electrons often have like chemical properties.

Electron configurations tin also predict stability. An atom is at its most stable (and therefore unreactive) when all its orbitals are full. The about stable configurations are the ones that have full free energy levels. These configurations occur in the noble gases. The noble gases are very stable elements that practise non react hands with any other elements.

Electron configurations tin can help to brand predictions about the ways in which certain elements will react and the chemical compounds or molecules that different elements will form. These principles aid to empathize the behavior of all chemicals, from the almost bones elements like hydrogen and helium, to the near complex proteins (huge biological chemicals made of thousands of different atoms bound together) found in the human body.

The Shielding Event and Effective Nuclear Charge

The shielding consequence, approximated past the effective nuclear charge, is due to inner electrons shielding valence electrons from the nucleus.

Learning Objectives

Calculate effective nuclear charges experienced by valence electrons.

Central Takeaways

Key Points

• The shielding effect describes the balance between the pull of the protons on valence electrons and the repulsion forces from inner electrons.
• The shielding issue explains why valence-shell electrons are more than easily removed from the atom. The event too explains atomic size. The more shielding, the farther the valence crush tin spread out and the bigger atoms will be.
• The constructive nuclear accuse is the cyberspace positive charge experienced past valence electrons. It can be approximated by the equation: Z_eff = Z – S, where Z is the atomic number and South is the number of shielding electrons.

Fundamental Terms

• cation: A positively charged ion, as opposed to an anion.
• valence crush: The outermost vanquish of electrons in an atom; these electrons take part in bonding with other atoms.
• valence trounce electron pair repulsion theory: A set of rules used to predict the shape of private molecules.
• core electrons: Those that are not part of the valence beat and as such, are not involved in bonding.
• nucleus: The positively charged cardinal part of an cantlet, made up of protons and neutrons.
• constructive nuclear charge: That experienced by an electron in a multi-electron cantlet, typically less for electrons that are shielded by core electrons.
• anion: A negatively charged ion, equally opposed to a cation.

The Shielding Consequence

Electrons in an atom can shield each other from the pull of the nucleus. This effect, called the shielding issue, describes the decrease in attraction between an electron and the nucleus in any atom with more than one electron shell. The more electron shells there are, the greater the shielding event experienced by the outermost electrons.

In hydrogen-like atoms, which accept just one electron, the cyberspace forcefulness on the electron is as large as the electrical attraction from the nucleus. Withal, when more electrons are involved, each electron (in the northward-crush) feels not only the electromagnetic attraction from the positive nucleus but also repulsion forces from other electrons in shells from i to n-1. This causes the net electrostatic force on electrons in outer shells to be significantly smaller in magnitude. Therefore, these electrons are not as strongly bound as electrons closer to the nucleus.

The shielding effect explains why valence crush electrons are more easily removed from the atom. The nucleus can pull the valence shell in tighter when the allure is strong and less tight when the attraction is weakened. The more than shielding that occurs, the further the valence shell can spread out. Every bit a result, atoms will be larger.

Example

Why is cesium bigger than elemental sodium?

The element sodium has the electron configuration 1s²2s²2p⁶3s¹. The outer free energy level is n = 3 and there is one valence electron. The attraction between this lone valence electron and the nucleus with 11 protons is shielded by the other 10 cadre electrons.

The electron configuration for cesium is 1s²2s²2p^vi3s^two3p^half-dozen4s²3d¹⁰4p^vi5s²4d¹⁰5p⁶6s¹. While there are more protons in a cesium atom, there are also many more than electrons shielding the outer electron from the nucleus. The outermost electron, 6s¹, therefore, is held very loosely. Considering of shielding, the nucleus has less control over this 6s^one electron than it does over a 3s^ane electron.

Effective Nuclear Charge

The magnitude of the shielding effect is difficult to summate precisely. As an approximation, we tin approximate the effective nuclear charge on each electron.

Effective nuclear charge diagram: Diagram of the concept of effective nuclear charge based on electron shielding.

The effective nuclear charge (ofttimes symbolized every bit Z_eff or Z*) is the net positive charge experienced by an electron in a multi-electron atom. The term "effective" is used considering the shielding issue of negatively charged electrons prevents higher orbital electrons from experiencing the full nuclear charge.

The constructive nuclear charge on an electron is given past the following equation:

Z_eff = Z – Due south

where Z is the number of protons in the nucleus (atomic number), and S is the number of electrons between the nucleus and the electron in question (the number of nonvalence electrons).

Instance

Consider a neutral neon cantlet (Ne), a sodium cation (Na⁺), and a fluorine anion (F^–). What is the effective nuclear accuse for each?

Start by figuring out the number of nonvalence electrons, which tin can be adamant from the electron configuration.

Ne has 10 electrons. The electron configuration is 1s²2s^two 2p^six. The valence shell is shell two and contains 8 valence electrons. Thus the number of nonvalence electrons is ii (10 total electrons – 8 valence). The diminutive number for neon is ten, therefore:

Z_eff(Ne) = x – 2 = 8+

Flourine has 9 electrons but F^– has gained an electron and thus has x. The electron configuration is the aforementioned equally for neon and the number of nonvalence electrons is 2. The atomic number for F^– is 9, therefore:

Z_eff(F^–) = 9 – ii = seven+

Sodium has xi electrons merely the Na⁺ ion has lost an electron and thus has 10. One time once again, the electron configuration is the same equally in the previous examples and the number of nonvalence electrons is two (by losing one electron, the valence beat out becomes the n=two beat out). The atomic number for Na⁺ is 11, therefore:

Z_eff(Na⁺) = xi – 2 = 9+

In each of the above examples (Ne, F^–, Na⁺) an atom has 10 electrons only the constructive nuclear charge varies considering each has a different atomic number. The sodium cation has the largest effective nuclear charge, which results in electrons being held the tightest, and therefore Na⁺ has the smallest atomic radius.

Diamagnetism and Paramagnetism

Diamagnetic atoms have just paired electrons, whereas paramagnetic atoms, which tin can be made magnetic, have at least ane unpaired electron.

Learning Objectives

Distinguish diamagnetic from paramagnetic atoms.

Key Takeaways

Key Points

• Any time two electrons share the same orbital, their spin quantum numbers take to exist different. Whenever two electrons are paired together in an orbital, or their total spin is 0, they are diamagnetic electrons. Atoms with all diamagnetic electrons are called diamagnetic atoms.
• A paramagnetic electron is an unpaired electron. An atom is considered paramagnetic if fifty-fifty one orbital has a net spin. An atom could have ten diamagnetic electrons, only equally long as it also has i paramagnetic electron, it is nevertheless considered a paramagnetic atom.
• Diamagnetic atoms repel magnetic fields. The unpaired electrons of paramagnetic atoms realign in response to external magnetic fields and are therefore attracted. Paramagnets do not retain magnetization in the absenteeism of a magnetic field, because thermal free energy randomizes electron spin orientations.

Cardinal Terms

• breakthrough number: One of sure integers or one-half-integers that specify the state of a breakthrough mechanical system (such every bit an electron in an atom).
• lanthanide: Whatsoever of the 14 rare globe elements from cerium (or from lanthanum) to lutetium in the periodic table. Considering their outermost orbitals are empty, they accept very similar chemistry. Below them are the actinides.
• diamagnetic: Materials that create an induced magnetic field in a management reverse to an externally applied magnetic field and are therefore repelled by the practical magnetic field.
• paramagnetic: Materials that are attracted past an externally applied magnetic field and class internal, induced magnetic fields in the management of the applied magnetic field.
• MRI: Magnetic Resonance Imaging, a medical imaging technique used in radiology to investigate the beefcake and physiology of the trunk in both wellness and illness.

Diamagnetism

Diamagnetic levitation: A small-scale (~6mm) slice of pyrolytic graphite (a fabric similar to graphite) levitating over a permanent gold magnet array (5mm cubes on a piece of steel). Notation that the poles of the magnets are aligned vertically and alternating (2 with north facing up, and two with southward facing up, diagonally).

Any time two electrons share the aforementioned orbital, their spin quantum numbers take to be different. In other words, one of the electrons has to exist "spin-upward," with [latex]m_s = +\frac{1}{2}[/latex], while the other electron is "spin-down," with [latex]m_s = -\frac{1}{two}[/latex]. This is important when it comes to determining the full spin in an electron orbital. In order to make up one's mind whether electron spins cancel, add their spin quantum numbers together. Whenever two electrons are paired together in an orbital, or their total spin is 0, they are called diamagnetic electrons.

Think of spins equally clockwise and counterclockwise. If one spin is clockwise and the other is counterclockwise, and then the two spin directions residue each other out and at that place is no leftover rotation. Note what all of this means in terms of electrons sharing an orbital: Since electrons in the aforementioned orbital always take opposite values for their spin quantum numbers (m_s), they will always end up canceling each other out. In other words, there is no leftover spin in an orbital that contains two electrons.

Electron spin is very important in determining the magnetic backdrop of an atom. If all of the electrons in an cantlet are paired up and share their orbital with some other electron, then the total spin in each orbital is cipher and the atom is diamagnetic. Diamagnetic atoms are not attracted to a magnetic field, merely rather are slightly repelled.

Paramagnetism

Electrons that are alone in an orbital are called paramagnetic electrons. Remember that if an electron is alone in an orbital, the orbital has a cyberspace spin, because the spin of the alone electron does not get canceled out. If even i orbital has a cyberspace spin, the entire atom will have a net spin. Therefore, an cantlet is considered to exist paramagnetic when it contains at least 1 paramagnetic electron. In other words, an atom could have 10 paired (diamagnetic) electrons, but equally long as it also has one unpaired (paramagnetic) electron, it is still considered a paramagnetic atom.

Merely every bit diamagnetic atoms are slightly repelled from a magnetic field, paramagnetic atoms are slightly attracted to a magnetic field. Paramagnetic backdrop are due to the realignment of the electron paths caused past the external magnetic field. Paramagnets exercise non retain any magnetization in the absence of an externally practical magnetic field, because thermal motion randomizes the spin orientations. Stronger magnetic effects are typically only observed when d- or f-electrons are involved. The size of the magnetic moment on a lanthanide atom can be quite big, as it tin acquit up to seven unpaired electrons, in the example of gadolinium(Three) (hence its utilize in MRI).

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