Amplitude of a wave is defined as the maximum peak of oscillation or vibration. Recall that frequency, wavelength, and speed are not dependent on the amplitude and are calculated using the wave equation:

Here, is the speed of the wave (which is the speed of light for electromagnetic waves), is the frequency, and is the wavelength. Amplitude of a wave is not present in this equation and, therefore, cannot be used to determine relative values of frequency, wavelength, and speed.

Amplitude of a wave is defined as the maximum peak of oscillation or vibration. Recall that frequency, wavelength, and speed are not dependent on the amplitude and are calculated using the wave equation:

Here, is the speed of the wave (which is the speed of light for electromagnetic waves), is the frequency, and is the wavelength. Amplitude of a wave is not present in this equation and, therefore, cannot be used to determine relative values of frequency, wavelength, and speed.

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).

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.

The phenomenon described in this question is called redshift and blueshift. All stars emit electromagnetic waves. The perceived wavelength of these waves depends on the relative motion of the object. If an object is approaching the observer (in this case, the earth) then the apparent wavelength of emitted waves decreases whereas if the object moves away then the apparent wavelength increases. This is called the Doppler effect.

To answer this question, we need to know the relative wavelengths of blue and red light. Blue light has wavelength between whereas red light has wavelength between . The question states that star A appears red and star B appears blue. Since red has the higher wavelength, star A is going away from the earth. Similarly, since blue has a lower wavelength, star B is approaching earth.

Recall that lower wavelength means higher frequency; therefore, blue has the higher frequency.

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.

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).

The phenomenon described in this question is called redshift and blueshift. All stars emit electromagnetic waves. The perceived wavelength of these waves depends on the relative motion of the object. If an object is approaching the observer (in this case, the earth) then the apparent wavelength of emitted waves decreases whereas if the object moves away then the apparent wavelength increases. This is called the Doppler effect.

To answer this question, we need to know the relative wavelengths of blue and red light. Blue light has wavelength between whereas red light has wavelength between . The question states that star A appears red and star B appears blue. Since red has the higher wavelength, star A is going away from the earth. Similarly, since blue has a lower wavelength, star B is approaching earth.

Recall that lower wavelength means higher frequency; therefore, blue has the higher frequency.

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.