the topic of this video is the bohr model the learning objectives are on the screen so before niels bohr developed what we now refer to as the bohr model uh there was no application of quantized energy states to build the model of of an atom such as the hydrogen atom there is no uh way to explain how there could be discrete energy states there so what the physicist kneels bohr proposed is that the energy quantization that we observe in different experiments like the photoelectric effect and also in black body radiation was a result of discrete energy states of electrons that are in orbit around a nucleus so what niels bohr derived independently of rydberg is an equation that looks like this one over lambda which is wavelength is equal to lowercase k this is a constant that i will give the numerical value for in a second that constant is divided by planck's constant multiplied by the speed of light another constant and as i write this out it should start to look familiar in that it has the overall same form as the rydberg equation that i previously discussed the value for the lowercase k here this particular constant is 2.179 times 10 to the negative 18 joules okay so uh the bohr model or niels bohr in in developing the model came up with this equation using first principles and what ended up helping get the attention of other scientists at the time was the fact that niels bohr had um come up with a an independent way of calculating what was known as the redbird constant and we still refer to it as the rydberg constant and the rydberg constant had been experimentally measured numerous times it was a very well known value um and so the fact that niels bohr came up with a way of using um fundamental constants to just to to calculate the rydberg constant um was considered a major success and brought a lot of attention to the bohr model so what does the bohr model uh look like essentially we have a positively charged nucleus and there are orbits around the nucleus in this particular case of the hydrogen atom um maybe i'll draw one more orbit these orbits as you get further and further away from the nucleus become higher and higher in energy so to distinguish orbits from another one another we give them numerical integer values one two and three the first numerical value n equals one this is what's referred to as the ground state this is the lowest possible energy state of an electron orbit now what can happen is you can excite an electron from the ground state up into an excited state and when this happens it happens at a very discrete energy that that is the exact energy difference between the n equals two excited state and the n equals one ground state so anything above n equals one okay is called an excited state that is these electrons in these uh orbits that are further and further away from the nucleus are at higher energies they are excited relative to the ground state okay so this can explain line spectra and how might it explain line spectra or specifically the line spectrum of hydrogen um rather than just arbitrarily assigning integer values like the rydberg equation did it just you know the rydberg equation just said okay well if we just use integer values not really knowing what those integer values correspond to we can recreate the the line spectrum of the hydrogen atom but what the bohr model says and what bohr said is well those integer values do have a meaning they have a meaning of discrete quantized energy states available to electrons in orbit around a nucleus so if we look over here in the case where electrons move to higher energy as light is absorbed this is the case where we start with an electron down here at the ground state n equals one light comes in and excites an electron to make and the electron can jump up it can jump up to the n equals two state or it could skip the n equals two state if the energy is high enough and it can go to the three four five in theory up infinitely many states uh uh but at some point the electron will escape the the the atom but that's a we don't need to go there yet um it's also important to note that you can also have excitations uh from not just the ground state but in excited state to other excited states okay and these are very discreet energy jumps now when we think about the line spectrum that is light that is emitted not light that was absorbed so in the line spectrum of hydrogen what we see are discrete energy bands and that is because the um electrons have been excited by electricity uh electrical energy up to a higher energy state and then they can relax back down so when the energy when the electron is in an excited state and drops back down to the ground state light is emitted and that light is emitted at an energy that corresponds to the difference between the excited state and whatever state it relaxed to so you can have a an electron go from any excited state directly to the ground state or you can also have these processes where an excited state will relax down to another excited state and again this will release energy that corresponds to the energy associated with that transition the other thing to point out here is an equation um that sort of uh captures this process so if we want to ever consider the the change in energy associated between these transitions all we have to do is uh consider this delta e this is just sort of a reworking of the equation i already put up is equal to that k constant that i mentioned uh multiplied by the this whole term which is 1 over n 1 squared minus 1 over n2 squared and this also by the way since this is an energy value is equal to hc over lambda okay so let's go ahead and put this uh to to practice and i'm going to scroll over to a practice problem that i have here so go ahead and pause the video now and you can write this out in your notes if you need to and i will go ahead and start solving it okay so what we need to do is find the energy in joules and the wavelength in meters of the line in the spectrum of hydrogen that represents the movement of an electron from the bohr orbit with n equals four to the bohr orbit with n equals six so we're going from an excited state of n equals four to an even higher excited state of n equals six so um the uh since we're start our starting point is n equals four this will be our n1 and our ending point and two is is going up to that n equals 6 level so i'm going to just go ahead and start by writing let's calculate the the change in energy for this jump from n equals 4 to n equals 6. so this is going to be equal to k times 1 over n 1 squared minus 1 over n 2 squared so this is going to be equal to 2.179 times 10 to the negative 18 joules and this is uh n one i said it's going to be four so that's four squared minus um one over n two squared so this is going to be six squared so uh this will give us 2.179 times 10 to the negative 18 joules multiplied by 1 over 16 minus 1 over 36 okay and if you do this and i encourage you to practice doing this in your calculator you should get an energy value of seven point five six six times ten to the negative twentieth joules so this answer does make sense just based off of the order of magnitude of that scientific notation it's a very small energy value um so now the that's the first part of the question uh the second part is what is the wavelength in meters and in what part of the electromagnetic spectrum do we find this radiation so let's go ahead and use the relationship between energy wavelength planck's constant and the speed of light so we know that wavelength is equal to hc over e so this is going to be equal to planck's constant 6.626 times 10 to the negative 34 joule seconds multiplied by the speed of light 2.998 times 10 to the 8th meters per second all over this energy value that we just calculated five six six times ten to the negative twenty joules always do a unit check to make sure this is cancel out joules we can sell joules seconds will cancel out with seconds we'll be left with units of meters which is exactly what we want and we should come up with a value of 2.626 times 10 to the negative 6 meters that's our answer now if we look back to what uh a figure that we uh that that shows different parts of the electromagnetic spectrum we'll see which region we find this value in so we're at about 2.6 times 10 to the negative sixth meters so this is a nice figure showing different parts of the electro electromagnetic spectrum we are at about right here we are at about an order of magnitude of 10 to the negative 6 meters for our wavelength so this puts us in the infrared