Nuclear, Quantum, and Molecular Chemistry - Physical Chemistry

Orbitals are regions in an electron shell where electrons might be located. There are several types of orbitals such as , and . Most elements found on the periodic table contain electrons within one of these orbitals. A characteristic of an orbital is that it can only contain two electrons maximum. A shell might contain multiple orbitals; however, each orbital can only contain two electrons. Each orbital has a unique shape that corresponds to the electron density (the possible location of an electron at a given point in time). The orbital has a spherical shape whereas the orbital has a dumbbell shape. As mentioned, a shell can contain multiple types of orbitals. A shell can typically contain one orbital, three orbitals, five orbitals, and seven orbitals. Remember that the shape of the orbital has no bearing on the amount of orbitals in a shell. An orbital is higher in energy if it is found farther away from the nucleus. The orbitals in order of increasing energy is as follows . Therefore, an orbital has lower energy than a orbital in the same shell.

To answer this question, we need to find the electron configuration of both elemental sodium and sodium cation. If we look at the periodic table we can see that sodium is found on the first column. Since it is found in the first column, sodium has one valence electron. To complete octet, sodium will readily lose an electron and become a positively charged sodium ion. The electron configuration for sodium is . The electron configuration for sodium ion is (because it lost its electron in the orbital). This means that elemental sodium has an unpaired electron in its orbital; the sodium ion has no unpaired electrons. Recall that an unpaired electron can generate its own magnetic field and is called paramagnetic; therefore, solid sodium is paramagnetic. The number of electrons in the orbitals for both sodium and sodium ion is the same (6 electrons total in the orbital). The outermost shell of sodium is the third shell (because sodium is located on the third row of periodic table). Elemental sodium contains one electron in the orbital in the outermost shell whereas the sodium ion contains 6 electrons in its outermost shell.

Hybridization is a process involving the fusion, or hybridization, of and orbitals to form a unique orbital. It is possible for various combinations of and hybridization. Recall that there is one orbital and three orbitals in each shell. This means that the one orbital can hybridize with 1, 2, or all 3 orbitals. Since there are three total combinations, there are three types of hybridized orbitals. These are , , and . orbital has one and one orbital hybridized. This means that the orbital and the first orbital become a new orbital. A molecule with hybridization will have two orbitals and two orbitals. Similarly, an orbital is made from the hybridization of one and two orbitals. In hybridization, there are three orbitals and one orbital. Finally, an orbital has one and all three orbitals; therefore, an hybridized molecule will have four orbitals and no orbitals. The question states that there are three hybridized orbitals in this molecule; therefore, this molecule must be hybridized. The single orbital is unhybridized because the molecule probably has a double bond. Electrons in bonds in double and triple bonds cannot be found in hybridized orbitals; therefore, they need their own orbital. If a molecule has one bond (double bond), then it will need one orbital and will be hybridized (because this will give three hybridized orbitals and one orbital). If it has two bonds (triple bond), then it will need two orbitals and will be hybridized. If a molecule has all bonds (single bonds), then the molecule will require no empty orbitals for the delocalized electrons, and will be hybridized.

Carbon tetrachloride, , has a central carbon atom attached to four chlorine atoms. The bonds between the carbon atom and chlorine atoms are single covalent bonds. The electrons in a single bond ( bond) can be found in hybridized orbitals. Since carbon tetrachloride only has single bonds, the carbon atom can hybridize all of its orbitals (one and three ) in the outermost shell and form a hybridization; therefore, three orbitals and one orbital participate in hybridization leading us to the correct answer. Carbon dioxide, , has a central carbon atom bonded to two oxygen atoms. To complete octet, carbon and oxygen atoms have double bonds. This means that carbon dioxide has two bonds (two double bonds). Recall that electrons in bonds cannot reside in hybridized orbitals; therefore, to accommodate the two bonds we need two empty, unhybridized orbitals. This means that carbon dioxide will have hybridization of one and one orbital, giving it an hybridization.

Photons are fundamental particles that make up electromagnetic waves (light). The key aspect of photon is that it has very high speed and no mass; therefore, mass for photons is always zero.

To solve this question, we need to use the equation relating energy of a wave to its wavelength.

Here, is the energy, is Planck’s constant, is speed of light (for us it’s always ), and is the wavelength (in meters). The energy of the ultraviolet rays is

If we look at the electromagnetic spectrum we will notice that the wavelength of radio waves is a lot higher than ultraviolet rays. Since energy is inversely proportional to wavelength we can conclude that the energy of radio waves is lower than ultraviolet's. The only answer choice with an energy lower than ultraviolet rays energy is 1.24neV.

Electromagnetic spectrum is a spectrum of different types of light. Each type of electromagnetic wave differs from one another based on the frequency and wavelength; however, the speed of every electromagnetic wave in air is . The wave equation relates the speed of an electromagnetic to its wavelength and frequency as follows.

Here, is speed of light, is wavelength, and is frequency. Since is always constant, wavelength and frequency are inversely proportional to each other. This means that if the wavelength increases the frequency decreases.

Since we're looking at the orbital, we know . The range of possible values for is 0 to . Possible values for range to . Therefore, among the answer choices, is the only possible combination of quantum numbers corresponding to an orbital.

Since we're looking at the orbital, we know . The range of possible values for is 0 to . Possible values for range to . Therefore, among the answer choices,

is the only possible combination of quantum numbers corresponding to a orbital.

The types of subshells, from smallest to largest, are as follows: s, p, d, and f. These four subshells correspond respectively to the following quantum numbers: 0, 1, 2, and 3. The total number of sublevels with n = 4 is n or 4: 4s, 4p, 4d and 4f.

Quantum numbers are fancy coordinate systems that describe the potential location of an electron within an atom. The first quantum number is called the principal quantum number and it signifies the shell the electron is located in. Recall that electron shells are discrete orbits in an atom that have discrete energy; therefore, the principal quantum number signifies the energy level of an electron.

The principal quantum number is always an integer and is always greater than zero. If the electron is found within the first shell, if then the electron is found within the second shell, and so and and so forth. Also, since it is always greater than zero, the principal quantum number can never be negative.

Potassium has one valence electron. This means that there is one electron in its outermost shell (4th shell). Potassium ion, on the other hand, loses an electron and has a complete octet (has eight valence electrons) in its 3rd shell. Recall that the principal quantum number signifies the shell. Since the valence electron of potassium is found in the fourth shell, . Similarly, the valence electrons of potassium ion are found in the third shell and for them. Valence electron of potassium has the higher principal quantum number.

Orbital angular momentum number () is the second quantum number and it signifies the type of orbital. It is always greater than or equal to zero. There are four main types of orbital: s, p, d, and f. Each orbital can hold two electrons. In a given shell, there are one ‘s’ orbital, three ‘p’ orbitals, five ‘d’ orbitals, and seven ‘f’ orbitals. ‘l’ = 0 for ‘s’ orbitals, ‘l’ = 1 for ‘p’ orbitals, ‘l’ = 2 for ‘d’ orbitals, and ‘l’ = 3 for ‘f’ orbitals. In potassium, there is only one valence electron; therefore, there is only one electron in the fourth shell and it can fit into the ‘s’ orbital. In potassium ion, there are eight valence electrons; therefore, two electrons can be found in the ‘s’ orbital and the remaining six electrons can be found in the three ‘p’ orbitals. Not all valence electrons of potassium ion and potassium have different ‘l’ value. This is because valence electron of potassium and two of the valence electrons of potassium ion are found in the ‘s’ orbital ().

Electrons found in higher shell numbers have higher energy. Valence electron of potassium is found in the fourth shell; therefore, it will have a higher energy than any of the valence electrons of potassium ion.

There are four quantum numbers. The first quantum, or principal quantum number, is designated by the letter ‘n’. It signifies the electron shell, or the energy level of the electron. The second quantum number, or orbital angular momentum quantum number, is designated by the letter ‘l’. It signifies the shape (or type) of the orbital. The third quantum number, or magnetic quantum number, is designated by . This signifies the energy level within a subshell. Each orbital can be located in different orientations in space. For example, each of the three ‘p’ orbitals are oriented differently in space and have different energy levels. The third quantum number describes this phenomenon. Finally, the fourth quantum number, or spin quantum number, is designated by and describes the spin of the electron. An electron can spin clockwise or counterclockwise. describes the direction of the spin. Since an electron can only rotate two ways, can only be two values or .

These four numbers together describe the potential location of an electron inside an atom. Note that no two electrons can have the same set of quantum numbers (meaning at least one of the four numbers will be different).

Ethene, or , has a carbon-carbon single () and double () bond. Recall that a bond can be found in hybridized orbitals whereas a bond cannot. This means that the carbon atoms in ethene hybridize the single ‘s’ orbital and two of the ‘p’ orbitals, forming a hybridization. The bonds () are found in these three hybridized orbitals. The remaining unhybridized ‘p’ orbital will house the two electrons in the bond.

The orbital angular momentum number is the second quantum number and it signifies the type of orbital. An electron found in a ‘p’ orbital will always have an . Since both electrons in the bond are found in the ‘p’ orbital, the ‘l’ value for both electrons is the same.

The principal quantum number is the first quantum number and it signifies the shell or energy level of an electron. All electrons involved in bonds are found in carbon’s outermost shell (2nd shell); therefore, they will all have an . Remember that no two electrons can have the same set of quantum numbers (regardless of whether the electrons are found as lone pairs, in bonds, or in bonds).

The principle quantum number (n) and the angular quantum number (l) are acceptable. However, the magnetic quantum number (m) is restricted to lie between -l and l. Therefore, for l=2, the only possible numbers for m are -2, -1, 0, 1, 2.

Emission is the process of releasing (or emitting) photons from an atom whereas absorption is the process of absorbing photons. After emission, the atom releases energy (in the form of photons) and goes to a lower energy state. In absorption, however, the atom absorbs energy and goes to a higher energy state. Recall that lower energy always means more stable; therefore, after emission, an atom or molecule goes to a more stable state whereas after absorption it goes to a less stable state.

To achieve an octet of valence electrons, atoms can share electrons so that all atoms participating in the bond will have full valence shells. Covalent bonds, by definition, result from the sharing of one or more pairs of valence electrons.

The key to this problem is that electrons in covalent bonds are shared and therefore "belong" to both of the bonded atoms. Sulfur is a nonmetal in group 6A , and therefore has 6 valence electrons. In order to obey the octet rule, it needs to gain 2 electrons . It can do this by forming 2 single covalent bonds.

The key to this problem is that electrons in covalent bonds are shared and therefore "belong" to both of the bonded atoms. Selenium is a nonmetal in group 6A , and therefore has 6 valence electrons. In order to obey the octet rule, it needs to gain 2 electrons. It can do this by forming 2 single covalent bonds.