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Electrorns in an atom 3re Mote Sabl than frec clecbrons The Eehy the cnergy leveh &l elettrers CAlam nentaiuc Itree eleciroo5 Afr Jctinco *hoytl energy af iero)...

Question

Electrorns in an atom 3re Mote Sabl than frec clecbrons The Eehy the cnergy leveh &l elettrers CAlam nentaiuc Itree eleciroo5 Afr Jctinco *hoytl energy af iero) Cskulate In0 enerey ol a hydrosen ectrc 7 /7 (hlCalcularcE 7erEYninttinieCalculnaeand54s well; Grah these energy levels Jallle Indudine n=5 IntOur Lncto fornzl 2 notebonk In scalc Sct the top linie t0 zero, the enerKy fa frec clectreni |a Intinily

Electrorns in an atom 3re Mote Sabl than frec clecbrons The Eehy the cnergy leveh &l elettrers CAlam nentaiuc Itree eleciroo5 Afr Jctinco *hoytl energy af iero) Cskulate In0 enerey ol a hydrosen ectrc 7 /7 (hl Calcularc E 7erEY ninttinie Calculnae and54s well; Grah these energy levels Jallle Indudine n=5 IntOur Lncto fornzl 2 notebonk In scalc Sct the top linie t0 zero, the enerKy fa frec clectreni |a Intinily



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For a certain atom, there are energy levels $A, B, C$ corresponding to energy values $t_{A}<E_{B}<E_{C}$. Choose the correct option if $\lambda_{1}, \lambda_{2}, \hbar_{3}$ are the wavelength of radiations corresponding to the transition from $C$ to $B$, $B$ to $A$ and $C$ to $A$ respectively : (a) $\lambda_{3}=\lambda_{1}+\lambda_{2}$ (b) $\lambda_{3}=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}}$ (c) $\lambda_{1}+\lambda_{2}+\Lambda_{3}=0$ (d) $3 \lambda_{2}=\lambda_{3}+2 \lambda_{2}$

Here we have to find out mhm binding energy of F E N B I for part the atomic number 26. And Mark somebody 56 4 E. So, the number of protons is that equal to 26? A number of neutrons is unequal to atomic mass number minus number of protons equal to 56 minus 26. Equal to 30. So mass defect will be equal to mps mass of a proton. I am in his massive neutron mm is massive. Nucleus mass of proton is 1.7825 atomic mass unit. Most of neutron is 1.8665 atomic mass unit minus nucleus Moss is 55.93 4939 He control 0.52 846 one atomic mass unit. Now binding energy is equal to Bill to em C square delta M s 0.528461 atomic mass unit. And one atomic mass unit is equal to 9 31.5 mega electron world. So in place of atomic mass unit, EU we liked this and multiplied by c square. This gives us 4 92.26 mega electron volt. As by nick energy of F E. Find. The energy part nuclear will be by negativity upon atomic mass number equal to 4 92 point 26 million electron volt 0.56 which is equal to 8.79 maybe. I looked on board but need clear on for part B we have atomic mass number 209 and atomic number 83. So the number of protons is equal to atomic number called to 83. And a number of neutron is atomic mass number minus atomic number equal to 209 minus 83 2. 126. No mass defect is equal to as above. Number of protons. Moss minus number of neutrons times mass of a neutron. Sorry, present minus mass of Nicholas. He put the values called to 1.760877 atomic mass unit. It's a mass defect. So binding energy is delta M C squared equal to 1.760 877 atomic mass unit can be written as 9 31 5 electron volt but she square she's quit. So this will give us by Nick energy as 1640 0.2 57 mega electron World binding energy part Nicolien is he upon atomic mass number? Atomic mass number is 209. So binding energy per nuclear is 7.85 mega electron volt. But nuclear by Nick energy this complete the solution. Thank you.

Socialist U. 19 energy of medium place is the energy of faster. It's just any state of like two plus. Is it is already tell you living in the question. So yeah, it is already in the hole in the book so we can refer from there, correct option. Will we see? Okay. Thank you.

The discretion. We are looking at the collision. Off to party goes right. We have our particle A This this the colliding particle, right. This, uh, energy connecting energy coming in with some velocity striking the stationary target X and, uh, we're gonna fight is theme the minimum. Can you take energy? That particle a must have in order for a nuclear reaction to proceed. Now, at this minimum energy condition, what we find is that the final states off the system must be an inelastic collision, right? Because only in this in the elastic collision condition, well, the maximum amount off kinetic energy be lost, all right into converting energy into the mass right, which is three nuclear reaction and therefore be can assume that's our particles because it is a completely, perfectly inelastic collision. They will move together with a single velocity after the collision. Every colored assemblies philosophies just BC so to start off, we use conservation of momentum for the entire system. We know that at the start, in more mentally system is Emma Times Va is it goes to the final momentum of the system, which is Emmy Times plus m x times, the sea now looking at energy conservation, we know that the initial energy initial kinetic energy is just half m a e a square. What about the final kinetic energy? So the final kinetic energy is half times are m a plus mx times V C square. What we want to do is to substitute in D. C. Right. So from this moment, um, conservation equation, we know that v c is at me over m e plus mx times fee a square. So to put that in, we here we have half m a square over Amy, plus m x times v a. Right. So one off the factors is gone because this common term over here is the same as the denominator. So they cancel, one of it cancels out. So we are left before the power one. You know, data. And what you see we're here. Is that if you do factor myself half m e p a square. You see that this is just the initial energy, right? So we can just replace this with e I. We're going to do a small trick over here using the previous understanding that I've explained that it's the energy the kinetic energy that is lost. It's lost its used to convert, right. Call it it in two mess right off the system. And this conversion into mass is basically the que value. All right, Thank you. Value off t entire nuclear reaction. This amount of kinetic energy loss must be equal to the Q value. How do you get kinetic energy lost from here? Right. What we're gonna do is going to subtract E I on both sides of the equation. So e f minus e i on the right hand side, we will have e i types this minus e. I just basically Yeah, I Emil for me plus m X minus one. Now what is strict does is that we can extract cue from here because this is essentially negative off the energy that is lost. Our energy loss is just e I minus E f, right? Yeah, I minus CF energy loss. So if you get the f minus here is negative off the energy lost, so in this case is negative. Cute for sure. And if you're to simplify this fraction Amy last MX minus one, you get MX over m E plus mx. So a negative MX now, to get final expression, we know that the initial energy alrighty. I is just the minimum amount off energy that you need, which is basically the trestle energy. Right? So therefore we can replace Oh, ei, it's just, uh, the special energy. And if you're the gary off the negative value Negative sign que. Now, remember, any starts over here the new correction ISS and do service and also make meaning that, uh, our que value itself is a negative value. Right? So But we need a positive value over here because we want our energy to be positive. So we are at a negative sign over here to make this and atomic direction to be a positive value. So this and atomic Because he said atomic, this will be a negative value. So negative negative become a positive failure. So dividing this factor over getting cute me plus m x over m x Jess the expression debts we want now to use this to calculate an actual example, we are given the William for alpha particle reacts with nitrogen. Give us oxygen oxygen 17 plus a proton. This case to find the treasure energy, we first need to find the value. Thank you. Very of destruction. We take the mass difference between the initial reluctance. Jeez, how far? Particle plus mess off, nitrogen minus away. Mess off oxygen 17 minus away. The mass of the proton multiplied by C square Just natural 0.5 MTV for you and this should give us about negative 1.19 MTV. So this the and automate direction Alright. So similar to our previous example, our previous policy question right requires and and ultimate direction eso Using this value, you can find the treasure energy taking the negative off the Q value. Jeez, 1.19 on your feet applied by one plus mass off the colliding particle, which is the offer particle divide by the mess off the target UK just the nitrogen. You should get about 1.53 MTV. So this 60 treasure energy

Use dimensional analysis to show that the expression for the energy levels of hydrogen, like atoms given by equation 7 25 has units of energy. So equation 7 25 is east to then is equal to negative K C E squared over H bar. Um you over two in squared. Okay, so using S. I. Units and noting that Z and N. R. Unit liss, so we need to know that as units of energies. That's a jewel. So the first one is newton meters squared over. Cool on squared for K. He is measured in here, she is cool um squared or columns. H bar is in units of jewels, time seconds, this is squared and here you have kilograms. So the sea squares will cancel a jewel is a newton times a meter. So we can do that on the right hand side. So newton meters squared over newton meter second squared kilograms. So the newton's cancels. And you get meters squared kilograms, meters squared kilograms over seconds. And since a kilogram meter per second is a newton, this is a newton meter which is equal to a jewel.


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