so uh this is very
similar to again the calculations that
you'll have to do
today in this experiment and obviously
in lecture as well
so let us take a look at perhaps the
first one
here get something to write with here
that might help
try that there we go all right so we
basically have an electron that's
transitioning
from um
the n equals five
energy level to the n equals two energy
level
and again just for orientation purposes
n equals five is higher in energy
obviously than n equals
two is lower in energy so this electron
is traveling
down in terms of energy and we'll see
what that all means in just a second
so whenever we're trying to figure out
the energy associated with that we're
going to use that equation that we saw
in lecture at the end there the change
in energy is minus
2.18 times 10 to the minus 18 joules
i'm gonna round that number just to make
it a little bit easier
one over n squared final
so the final guy minus one over
n squared initial so your initial
uh um
energy level so we could calculate right
off the bat the change in energy here
gonna be minus 2.18 times 10 to the
minus 18
joules our final is actually
2 here right so that's our final
so 1 over 2 squared is 4
one over four and one over our
initial which was five will be
twenty-five actually square at this time
i think i did it the first time
and if we do all that good stuff there
we're going to take 1 divided by 4
minus 1 divided by 25 and
times it by 2.18 to the minus 18
looks like it will get us something like
we'll go
4.5 times 10 to the minus 19
joules and it will be negative in this
case
and that makes sense as what we were
just talking about again that electron
is going from higher energy
to lower energy so what it has to do is
give off that energy in the form of a
photon
and that would mean that it is
exothermic in this case again
negative value for our energy any
questions so far
on that particular one
now we want to also find the
wavelength and the frequency so remember
that our
e here is equal to h
times the frequency it also equals
hc over the wavelength and it also
equals obviously this number
here so we can use our
e is equal to h times the frequency this
is one way we can get the frequency
and that means that the frequency would
be
e divided by h when we divide the h to
the other side
now this is what i was talking about
previously at the end there
our energy is negative and you should
leave it as
a negative number uh for the energy
value
but when we continue on to use it here
to calculate something like frequency
our wavelength we want to get rid of the
negative so we do not get a negative
value
so we're just going to use the positive
version here
4.58 times 10 to the minus 19 joules
we're going to divide it by planck's
constant which is that 6.63
times 10 to the minus 34 joule seconds
joules are going to cancel each other
out going to leave us with reciprocal
seconds
and that will leave us with
and divided by 6.63 minus 34.
looks like we get a frequency of
6.91 times
10 to the 14. again here reciprocal
seconds
which is a hertz would be our frequency
in this particular case
now because we now have the frequency
and honestly we have the energy as well
to get to the wavelength you can really
do it two ways you could use
e is equal to hc over the wavelength
and the wavelength equals hc over the
energy
r because we now have the frequency you
could also use c is equal to the
wavelength times the frequency
or the wavelength is equal to c divided
by the frequency
i'll do both ways here so you can see
you should hopefully get the same answer
so if you did uh 3 times 10 to the 8
meters per second which is c divided by
our frequency which is 6.91 times 10 to
the 14
reciprocal seconds uh we will end up
with
four point three four times ten to the
minus seven
meters and remember that we want to go
to nanometers so there are ten to the
minus nine
meters in a nanometer so we want to
divide that by 10 to the minus 9 or 1
times 10 to the minus 9.
and again make sure you use your
exponent button get you
434 nanometers
as our wavelength again here you could
have went into this one as well
and this would be the wavelength is
equal to our planck's constant
joule seconds our speed of light
and through our energy in here also
making sure you use it as a
positive number not the negative number
joules will cancel seconds will cancel
we'll leave you with meters at that
point and what you will get
is hopefully the same number
you always want um wavelength and
nanometers
uh not always in this particular case we
do because we're talking about the
visible part of the spectrum
so it usually is very commonly in
nanometers in this case
if it really doesn't specify you could
leave it in any unit you want
but that's usually why we kind of went
to nanometers here and then obviously we
got the same number as you can see
and it would convert obviously into the
same number in terms of
nanometers questions on any of that
going back to
um frequency yeah um is it ever
negative no so uh you always want to
make sure
the frequency and the wavelength should
always be positive numbers
and what usually happens is people
forget to get rid of the negative there
on the energy
and that's where the usual end up with
that negative value so
it is important though like i mentioned
to keep the negative
on the energy because it does indicate
whether or not it's exothermic or
endothermic in terms of the energy part
for the atom
uh but you definitely should just make
it a positive number if you're going to
carry on with it to do something like
wavelength or frequency
and those should always be positive
numbers other questions
so just for reference point in terms of
uh 434 nanometers if you kind of look in
the visible part of the spectrum
we're shooting like blue in terms of
that color
so this is a blue all right let's take a
look at the next one which should be a
very similar type calculation here
for b we're going from n is equal to
four uh to n is equal to
two so we'll start with the same part of
the calculation there
we're going to use that energy equation
and our final
minus initial to figure out
uh the change in energy that's really
happening with the atom
so again here we are going from four to
two
so that's higher energy level to lower
so much like what we saw in the previous
one
we could predict that the energy change
should be
negative here for our atom so minus 2.18
times 10 to the minus 18.
our final is our 2 here
so again that's going to be 1 over 4.
our initial is going to be n equals 4 so
4
squared is 16 and if we do that
we'll get 1 divided by 4 minus 1 divided
by 16
times 2.18 to the minus
that's going to give us an energy here
for the atom again
minus which is what we predicted 4.09
times 10 to the minus 19
joules so again here we do want to keep
the negative for our energy
because that tells us like we would
predict again the electron is
dropping energy which means for the atom
it's got to give
off that energy so it'll be exothermic
for the atom there
and again that's why we have that
negative number happening
and here again we have a couple of ways
we could get to the remainder of
the answers we again could do the same
thing for the frequency
e is equal to h times the frequency
which means the frequency is
energy uh divided by planck's constant
so here again we're going to get rid of
the negative because we want to make
sure that we do end up with a positive
number
and our h again is a constant 6.63
times 10 to the minus 34 joules times
seconds
again the joules are going to cancel
that's going to leave us with our
reciprocal seconds
and as i mentioned earlier today you
want to definitely make sure you are
using your exponent button on your
calculator
or again you will be finding yourself
like off in terms of your numbers
so again if your numbers are very close
the front part but this part not so good
probably the way you're putting it into
your calculator so we get 6.17 times 10
to the 14 again the units here are
reciprocal seconds
as our frequency
and lastly at this point now that we
have the frequency for example we can
use
this equation here if we like to figure
out the wavelength the wavelength would
be
c divided by the frequency so again c
being a constant 3 times 10 to the 8th
meters per second divided by our
6.17 times 10 to the 14 reciprocal
seconds
again our second is going to cancel and
this will give us our wavelength
in meters and if we do that
looks like we get something like uh 4.87
on some rounding times 10 to the minus 7
meters and again here since we are in
the visible part of spectrum and talking
about colors
we want to convert it to nanometers so
again
10 to the minus 9 meters is a
nanometer and we would divide that by
1 times 10 to the minus 9 and that's
going to give us 400
and we'll round it to 487
nanometers as our wavelength
any questions on those there
and again you might end up with 46 if
you did a little bit more rounding than
i did
it's okay and in terms of color this is
somewhere near green
in terms of color where it's coming off
any questions on that particular one
um do you always convert it to
nanometers at the end
uh you don't always have to convert to
nanometers uh typically
if it's uh if it's in that visible part
of the spectrum so that visible part of
spectrum is where we
see color right so that's where that
roygbiv is
and typically when the wavelengths given
for that part of the spectrum
because they're kind of small numbers
and used a lot they're usually given in
nanometers
but they don't have to be so again if it
doesn't specify
uh you could have left it in meters it
would have been perfectly fine
okay thank you you're welcome other
questions
okay so one last one there
uh we are transitioning from
where we're transitioning from we are
going three to two here
so again following sort of the same
thing we've been doing
n is equal to three
and is equal to two so still the same
sort of transition
going down in energy so we can't predict
that our energy here
should be negative for the atom as it
should be given off that energy to allow
the electrons to drop down
and rolling through our calculation here
minus 2.18 times 10 and minus 18 which
again
is a constant that's that rydberg's
constant in case you ever need to find
it by name
our final here is going to be 2 so 2
squared will give us
4 minus 1 over our initial squared which
is
3 so that's going to be 9 in terms of 1
of squaring it so 1 divided by 4
minus 1 divided by 9 times 2.18
to the minus 18 gonna give us 3.03
also going to be negative here 3.03
times 10 to the minus 19
joules and again as we talked about
their negative which is what we would
expect to happen
and we will then go with the frequency
like we've been doing so e is equal to
h times frequency so our frequency being
e divided by h and that's going to give
us
again using the positive value here
divided by our constant
again joule is going to cancel gonna
leave us with reciprocal seconds ra
hertz
and um 6.63
minus 34. gonna give us uh 4.57
times 10 to the 14 reciprocal seconds
the same thing as a hertz and again here
one way to get to
wavelength is to use the same one that
we've been using
again just like we did on the first one
you could if you wanted to
just went right to wavelength using that
one as well
and again wavelength here would be c
divided by frequency
so 3 times 10 to the 8th
meters per second and our frequency of
4.57 10 to the 14
reciprocal seconds seconds gonna cancel
and we will end up with
looks like uh 6.57
times ten to the minus seven meters
and again doing our conversion to
nanometers since i asked you to do that
and you'll have to do that a lot in this
lab as well
we're going to divide it by 10 to the
minus 9.
and it looks like we end up with 657
nanometers here and for reference that
is sort of red orange orange red type
color
and in terms of uh the other question i
was actually asked is
what transition resulted in the longest
wavelength of light
and that would be our
c transition our c transition had the
longest wavelength 657 nanometers
versus i think was 486 versus
434 and again we would expect that based
on what we talked about
this transition is uh one energy level
which
is the lowest amount of energy of all
three of those transitions over there
lowest energy should correspond to
longest wavelength
the shortest wavelength which is the 434
transition
uh the five to the two should also
result in the
highest energy right because that's
again shorter wavelength
highest in energy also probably should
be highest in frequency as well
in terms of that when you compare your
numbers
so again any questions on any of these
sort of calculations clearly you need to
be able to
do these calculations the lab for
tonight is pretty much
all these calculations a whole bunch of
them any questions on any part of that
and as you can see there are some
multiple ways you could calculate it
for example for the wavelength you could
use the energy value if you want you
could then
or get the frequency like we did on some
of these and then get the wavelength
you know whichever way you want to kind
of do it you could alternatively get the
wavelength first and then get the
frequency so you can do it that way as
well
so there are a few different ways you
can kind of get there
again providing that you punch all these
numbers in correctly
you should end up with the same number
no matter which way you went
and again if you're finding yourself off
on any of these numbers
especially the exponent part my guess is
it's how you're punching it into your
calculator
