To solve this problem, we use the following equation:

Where  is the wavelength and  is the frequency.

Wavelength is given, and as we are dealing with the electromagnetic spectrum, we know that  is equal to the speed of light, which is given. We need to solve for frequency, so we arrange the equation as follows: 

Plug in known values and solve.

To solve this problem, we use the following equation:

Where  is the wavelength and  is the frequency.

Wavelength is given, and as we are dealing with the electromagnetic spectrum, we know that  is equal to the speed of light, which is given. We need to solve for frequency, so we arrange the equation as follows: 

Plug in known values and solve.

To solve this problem, we use the following equation:

Where  is the wavelength and  is the frequency.

Rearrange the equation to solve for wavelength.

Plug in known values and solve.

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 orbitals in an atom with n = 3 is 3² or 9: one 3s , three 3p and five 3d. Each orbital can hold a maximum of 2 electrons. Therefore, the maximum number of electrons possible is 2 x 9 = 18.

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 orbitals in an atom with n = 4 is 4² or 16: one 4s , three 4p , five 4d and seven 4f. Each orbital can hold a maximum of 2 electrons. Therefore, the maximum number of electrons possible is 32. 

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.

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).