Question Video: Determining the Number of Orbitals in a Shell Given the Principal Quantum Number | Nagwa Question Video: Determining the Number of Orbitals in a Shell Given the Principal Quantum Number | Nagwa

# Question Video: Determining the Number of Orbitals in a Shell Given the Principal Quantum Number Chemistry • Second Year of Secondary School

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What is the number of orbitals in the shell that has the principal quantum number π = 1?

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### Video Transcript

What is the number of orbitals in the shell that has the principal quantum number π equals one?

Inside of an atom, electrons are found in various energy levels called shells. The principal quantum number π represents the shell where the electron is found. π can be any positive integer. As π increases, the electron will be at a higher energy and less tightly bound to the nucleus.

Shells consist of one or more subshells. Subshells are described by the subsidiary quantum number π. The number of subshells within a shell depends on the principal quantum number. For a given value of π, π can be any integer from zero to π minus one. Each subsidiary quantum number corresponds to a different type of subshell, with s, p, d, and f being the most common that weβll encounter.

Each subshell is composed of one or more different orbitals. The orientation of these orbitals can be described using the magnetic quantum number π subscript π. The number of orbitals in a subshell depends on the subsidiary quantum number. For a given value of π, π subscript π can be any integer from negative π to positive π.

With all of this information in mind, letβs return to the question. We are told in the question that a shell has the principal quantum number of one. The subsidiary quantum number can be any integer from zero to π minus one. So zero is the only possible value for the subsidiary quantum number when π equals one. So this shell only contains one subshell, the s-type subshell. The magnetic quantum number can be any integer from negative π to positive π. So, when π equals zero, π subscript π can only equal zero. The single magnetic quantum number indicates that this subshell only contains one orbital. This lone orbital is an s orbital, which is spherical in shape.

From this, we can see that a shell with the principal quantum number of one contains a single subshell that contains a single orbital. So the number of orbitals in the shell that has the principal quantum number π equals one is one.

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