### Video Transcript

In the Bohr model of the atom, what
is the magnitude of the angular momentum of an electron in a hydrogen atom for which
𝑛 equals two? Use a value of 1.05 times 10 to the
negative 34 joule seconds for the reduced Planck constant.

So in this question, we’re
considering a hydrogen atom, and we’ve specifically been asked to use the Bohr model
of the atom. We can recall that a hydrogen atom
just has one proton in the nucleus and one electron and the Bohr model describes
atoms as consisting of electrons making circular orbits around the nucleus. So we can visualize this hydrogen
atom like this. Here’s the nucleus, and here’s an
electron making a circular path around it.

Let’s also recall that the Bohr
model actually only makes accurate predictions for single-electron systems, which is
why we’re being asked about hydrogen atom in this question. We’re being asked to find the
angular momentum of an electron for which 𝑛 equals two. Let’s recall that 𝑛 is the
principal quantum number of an electron. And it describes the energy level
that the electron occupies. So an electron in the lowest
possible energy level would have 𝑛 equals one. And in the Bohr model, this would
refer to the innermost orbit around the nucleus.

In this question, we’re told that
our electron has 𝑛 equals two, which would mean, according to the Bohr model, our
electron occupies an orbit that’s further away from the nucleus. The Bohr model gives us a simple
way of calculating the angular momentum of an electron in a hydrogen atom as long as
we know what its principal quantum number is. In other words, we can find its
angular momentum if we know which energy level it’s in.

This is given by the equation 𝐿
equals 𝑛ℎ bar, where 𝐿 represents the angular momentum of an electron, 𝑛
represents the principal quantum number, and ℎ bar is the reduced Planck
constant. And we’re told in the question that
this constant takes a value of 1.05 times 10 to the power of negative 34 joule
seconds. We should note that even though
it’s more common to express angular momentum in units of kilograms meters squared
per second, these units are actually equivalent to the units of the reduced Planck
constant.

Since the principal quantum number
𝑛 is dimensionless, this means that the units on the left and the right of the
equation are equivalent. Since we’re looking to calculate
the angular momentum and angular momentum is already the subject of this equation,
all we need to do is multiply the principal quantum number of our electron by the
reduced Planck constant. This gives us an angular momentum
of two times 1.05 times 10 to the negative 34 joule seconds, which gives us a value
of 2.10 times 10 to the negative 34 joule seconds. And this is the final answer to the
question. In the Bohr model of the atom, the
magnitude of the angular momentum of an electron in a hydrogen atom for which 𝑛
equals two is 2.10 times 10 to the negative 34 joule seconds.