Question Video: Determining the Number of Possible Values of 𝑙 When 𝑛 = 1 | Nagwa Question Video: Determining the Number of Possible Values of 𝑙 When 𝑛 = 1 | Nagwa

Question Video: Determining the Number of Possible Values of 𝑙 When 𝑛 = 1 Chemistry • Second Year of Secondary School

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If 𝑛 = 1, how many possible values of 𝑙 are there?

02:12

Video Transcript

If 𝑛 equals one, how many possible values of 𝑙 are there?

Firstly, 𝑛 is the principal quantum number. 𝑛 determines the size of an atomic orbital. 𝑛 can only be a positive integer from one to seven. If we compare the spherical 1s and 2s orbitals, the 2s orbital is larger. It’s important to remember that 𝑛 also tells us the energy level in which an electron is found.

Now, the quantum number 𝑙 has a few names: the subsidiary, azimuthal, or orbital angular momentum quantum number. In this video, we will refer to 𝑙 as the subsidiary quantum number. This quantum number describes the shape of an atomic orbital. 𝑙 can have integer values from zero to 𝑛 minus one. The following table shows the type of orbital associated with each 𝑙-value. s orbitals are spherical, while p orbitals are dumbbell shaped. The shapes of d and f orbitals are far more complex and difficult to draw.

Now, let’s practice determining the possible values for 𝑙 when given a value for 𝑛. Let’s do this for only the first three energy levels.

If 𝑛 is three, 𝑙 has values from zero to 𝑛 minus one, which means the possible values of 𝑙 are zero, one, and two. We can see that each 𝑙-value corresponds to the type of subshells that the third energy level contains. If 𝑛 is two, there are only two possible values for 𝑙, which correspond to the 2s and 2p subshells inside energy level two. Finally, if 𝑛 is one, the only possible value of 𝑙 is zero, and the first energy level contains only the 1s subshell.

In conclusion, if 𝑛 equals one, there is only one possible value for 𝑙.

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