Question Video: Ranking Three Electrons from Lowest to Highest Energy Given the Quantum Numbers of Each | Nagwa Question Video: Ranking Three Electrons from Lowest to Highest Energy Given the Quantum Numbers of Each | Nagwa

Question Video: Ranking Three Electrons from Lowest to Highest Energy Given the Quantum Numbers of Each Chemistry • Second Year of Secondary School

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The quantum numbers for three electrons in an atom of silicon are shown. What is the correct order from lowest to highest energy of these electrons? 1. 𝑛 = 2, 𝑙 = 1, π‘š_𝑙 = +1, π‘š_𝑠 = βˆ’1/2 2. 𝑛 = 3, 𝑙 = 1, π‘š_𝑙 = βˆ’1, π‘š_𝑠 = βˆ’1/2 3. 𝑛 = 2, 𝑙 = 0, π‘š_𝑙 = 0, π‘š_𝑠 = +1/2

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Video Transcript

The quantum numbers for three electrons in an atom of silicon are shown. What is the correct order from lowest to highest energy of these electrons? (1) 𝑛 equals two, 𝑙 equals one, π‘š subscript 𝑙 equals positive one, π‘š subscript 𝑠 equals negative one-half. (2) 𝑛 equals three, 𝑙 equals one, π‘š subscript 𝑙 equals negative one, π‘š subscript 𝑠 equals negative one-half. (3) 𝑛 equals two, 𝑙 equals zero, π‘š subscript 𝑙 equals zero, π‘š subscript 𝑠 equals positive one-half. (A) (3), (2), (1); (B) (1), (2), (3); (C) (3), (1), (2); (D) (2), (1), (3); or (E) (2), (3), (1).

We have been given a set of quantum numbers for three electrons in an atom of silicon. We need to use these quantum numbers to rank the electrons in order from lowest to highest energy. Quantum numbers are values that can be used to completely describe an electron in an atom. The first quantum number is the principal quantum number given the symbol 𝑛. This quantum number indicates which electron shell or energy level the electron can be found in. The principal quantum number can be any positive integer. As 𝑛 increases, the electron will be at a higher energy and less tightly bound to the nucleus.

If we look at the principal quantum number of the three electrons, we can see that electron number (2) has the highest principal quantum number and will therefore have the highest energy. As we need to rank the electrons from lowest to highest energy, we can already eliminate answer choices (A), (B), (D), and (E) as none of these answer choices list electron number (2) as the electron with the highest energy. But to make sure that the electrons are listed in the correct order in answer choice (C), let’s take a look at the rest of the quantum numbers.

The next quantum number is the subsidiary quantum number, denoted with a lowercase 𝑙. This quantum number indicates the type of subshell that the electron is in. The subsidiary quantum number can be any positive integer from zero to 𝑛 minus one with each value representing a different subshell. The four most relevant types of subshell are s, p, d, and f. For the same principal quantum number value, an s-type subshell will have the lowest energy and an f-type subshell will have the highest energy of the four, so four electrons which have the same principal quantum number. The energy of the electron will increase with increasing subsidiary quantum number.

As we already know that electron number (2) has the highest energy, we need to compare the energies of electrons number (1) and (3) which have the same principal quantum number. We can see that electron number (3) has a subsidiary quantum number of zero, which corresponds to an s-type subshell, the lowest energy subshell for this principal quantum number. So we have confirmed that electron number (3) should have the lowest energy while electron number (2) has the highest energy.

The remaining two quantum numbers, the magnetic quantum number, which represents the orientation of the individual atomic orbitals in a subshell, and the spin quantum number, which represents the spin of an electron in an orbital, only affect the energy of an electron when the electron is in a magnetic field. So we don’t need to look at these quantum numbers to determine the correct answer. Therefore, using the quantum numbers for three electrons in an atom of silicon, the correct order from lowest to highest energy of these electrons is answer choice (C): (3), (1), (2).

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