Question
Which energy level does an electron move to if the electron is in the "n' 4 level of an H atom and emits photon of wavelength 954 nm;
Which energy level does an electron move to if the electron is in the "n' 4 level of an H atom and emits photon of wavelength 954 nm;
Answers
An electron in the $n=5$ level of an $\mathrm{H}$ atom emits a photon of wavelength $1281 \mathrm{nm}$. To what energy level does it move?
Hi, everyone. I'm here with problem 32 from chapter seven in this problem were given an electron that transitions from the N equals five state to an unknown level. And we're also told that the wavelength is 97.2 nanometers and were asked to find this unknown transition level. Well, how can we do this? Well, we can relate it back to rid Burke equation. And we know the red burger equation is one over the wave. White is equal to our times one over and one squared minus one over and two squared. And we know the end to must be greater than and one We're told in this equation that the electron is admitting. So we know in a mission that we're moving from a higher energy level to a lower energy level. So we know that if and to has been greater than and one that, and to is going to be our n equals five state and we must solve for n equals one state. So now let's plug in all over known values. We know that where a wave like is 97.2 nanometers, but we cannot forget to convert so have included our conversion factor. So then we can take 97.2 now two meters and multiply by one meter all over one times 10 to the nine Nana meters. And we set this equal to a Richburg constant times one over and one for a no squared minus. One over five squared. So now let's isolate are unknown variable by dividing both sides by our So if we divide besides by our one of getting 0.9 38 is equal to one over on one squared, minus 1/5 squared. So now if we move or if we add 1/5 square to those sides, we'll get 0.9 78 is equal to one over and one squared. And so now to get and one squared by itself, we're gonna multiply each side by an over one squared, which will give us and one squared is equal to one point. Oh, to which we can say is about one and then we'll square root both sides to give us our final cancer of N one is equal 21
Particular case, the electron in a ground state Adam move absorbs a proton of the wavefront 97.2 nanometers. So first fall, In order to solve this, we convert this two meters, which is gonna be 9.72 times 10 to the power of negative eight meters. So from here, this is going to correspond to the X rays in this particular case. So X rays and therefore, um, it's going to correspond to the values of and equal southern.
Fellow students in this question, we have to determine the wavelength lambda of the light amateur. When electron in the hydrogen atom undergoes transition from N equals to four, suppose initially state and two and finally equals two and equals two And finally equals two. Okay, so we can use the Red Bird formula. So we know that the wave number or one by lambda, it is equal to red bird number R. And one divided by and finally squared minus one by an initial square. Here, Red Bird Number is 1.097. My pleasure by 10 to the Power seven. And this is in the meter universe and one by and final which is equal to two. So two squared minus one by an initial which is four. So this four is square. So we get 1.097 player bait into the power seven and this is one by four and this will become one by 16. Okay, so after solving this, we will obtain that. This is equal to three by 16. Okay, now wavelength lambda, this value will be equals to the 16 divided by 1.97 multiplied by 10 to the power seven multiplied by three. So from here the wailing clammed up, it is equal to the 4.86 Mercury related to the power minus seven. Or it can meet her, or it can be written as 4 86 9 m. Okay, so this becomes the answer for this question. Okay, thank you.
For this question, we're asked to consider energy level that has a diameter d of 5.18 nanometers, which I convert two meters on. It wants to know what is the energy level and the hydrogen atoms. So ah, bores radius and the hydrogen atom a not is equal to 5.24 times in the minus. Excuse me 5.29 times 10 to the minus 11 meters. And the equation that ah, that governs the radius of the hydrogen atom R is equal to n squared where in is the order of the energy level times a nod and a non is bores radius. But of course, we know just from basic mathematics that the diameter of a knob checked if we treated as a circle is equal to two times that objects radius. So if you plug in that value for our, uh, this is equal to two times in squared times bores radius a. Not it is what we want. So we just need to simply solve this equation for in when we find that in is equal to thes square root of the diameter D divided by two times the Boers radius A not so plugging in our values for the Boers. Radius and diameter. Of course, in has to be, uh, an integer value. So we're gonna round and we want around down to the nearest integer value. Uh, it comes out to be 7.19 but of course, we're just going around the seven. So this is approximately seven. So in is equal to seven now, it's a solution.