Video Transcript
What is the number of orbitals in
the shell that has the principal quantum number 𝑛 equals one?
Inside of an atom, electrons are
found in various energy levels called shells. The principal quantum number 𝑛
represents the shell where the electron is found. 𝑛 can be any positive integer. As 𝑛 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 𝑙. The number of subshells within a
shell depends on the principal quantum number. For a given value of 𝑛, 𝑙 can be
any integer from zero to 𝑛 minus one. Each subsidiary quantum number
corresponds to a different type of subshell, with s, p, d, and f being the most
common that we’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 𝑚 subscript 𝑙. The number of orbitals in a
subshell depends on the subsidiary quantum number. For a given value of 𝑙, 𝑚
subscript 𝑙 can be any integer from negative 𝑙 to positive 𝑙.
With all of this information in
mind, let’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 𝑛 minus one. So zero is the only possible value
for the subsidiary quantum number when 𝑛 equals one. So this shell only contains one
subshell, the s-type subshell. The magnetic quantum number can be
any integer from negative 𝑙 to positive 𝑙. So, when 𝑙 equals zero, 𝑚
subscript 𝑙 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 𝑛 equals one is one.
