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The smallest emission of energy between adjacent states in neutral hydrogen atom comes from which of the following transitions?n =4-n=5n=1-n=2All of these transitio...

Question

The smallest emission of energy between adjacent states in neutral hydrogen atom comes from which of the following transitions?n =4-n=5n=1-n=2All of these transitions correspond to equal energies_n =5->n =4n =2-n=1

The smallest emission of energy between adjacent states in neutral hydrogen atom comes from which of the following transitions? n =4-n=5 n=1-n=2 All of these transitions correspond to equal energies_ n =5->n =4 n =2-n=1



Answers

(I) For the three hydrogen transitions indicated below, with $n$ being the initial state and $n^{\prime}$ being the final state, is the transition an absorption or an emission? Which is higher, the initial state energy or the final state energy of the atom? Finally, which of these transitions involves the largest energy photon? (a) $n=1, \quad n^{\prime}=3$ (b) $n=6, \quad n^{\prime}=2(c) n=4, \quad n^{\prime}=5$

Hello. Students. In this question, we have to determine which of the following electron transition electron tarnation in hydrogen atom will require the largest amount of energy. That is the key must be positive here. Okay, so we can see from the option A from N equals 212 N equals to this energy will be maximum from the Cuban options and this will be also positive. And in the option C from N equals 252 N equals to one. This energy will be negative. Okay? So but the if we talk about the magnitude then this will be the largest magnitude but it is in the negative. So it is not absorbing the energy. So this is the leasing energy and this is the absorbing energy. So hydrogen atom is requiring energy. So it means it must absorb some energy. Okay, So hence from the given options option A is the correct answer for this problem. Okay, in the rest of the options, the energy difference is not greater than these values. So this is the largest absorb energy for the hydrogen atom from the given options. Okay, thank you.

This problem. We're told that we have an electron transition in the hydrogen atom, were given four of these transitions and were asked which of them requires the most energy to be absorbed by the hydrogen atom in order for it to occur. The easiest way to do this is to refer to an energy level diagram for hydrogen transitions in this case, and here refers to the energy level states like so so were provided with four possible transitions. First is in equals. One tow n equals two Second is an equals two. Two n equals four the third and equals three. Two n equals nine in the fourth equals 10 tau equals one. The first thing to notice in this problem is that were asked, which transition requires the most energy to be absorbed. When we absorb energy, we are transitioning toe Ah, higher energy level. This allows us to actually eliminate choice D off the bat because in choice d, we're going from level 10 to level one, in which case we would release energy so we can eliminate choice d off the back. By looking at this diagram, you can see that the energy required for each successive energy level in order to increase our energy level of our electron decreases roughly exponentially. So choice A. For instance, the transition between level one and two is fairly large. The transition between two and four, as in choice be looks about like that. A transition between three and nine or choice See, is something like this. A visual inspection alone will tell you that the first transition from level 1 to 2 is in fact uh huh, the transition that requires the most energy. In order for the electron to complete it, calculations would also support support this conclusion.

Okay, so we're in chapter 37 54. So it says for three hydrogen transitions indicate below with n being the initial states in prime being final state, um is the transition and absorption our mission, which is the higher initial state energy or the final state energy in which of these transitions involves the largest energy. Okay, So to start out, we should know that the energy level energy of a level in is given in the Bohr model was given by the Rittenberg Negative Rittenberg Constant 13.6 TV over and squared. So her part, eh, It says in equals one to an n prime three. Well, based on this equation here, we should see that by her energy levels are going to have higher energies because of this negative, right? So you think of the other way around, cause in squared is on bottom, greater and squares with lower number. But since it's negative, it's actually a higher energy. So if in prime is our higher state that we know this is absorption, cause we're going from a lower energy toe, a higher energy. Um, so now we can find the photon energy, which is just the energy difference between these so energy of the Proton. It's just energy of level three, minus energy of level one. Well, let's write that out. That's negative. 13.6 E v times one over three squared, minus one over one square. If this comes out to being 12.1 TV for the energy of the symptoms, Good Barbie Party says in equal six. And we're going to a in prime of two. Well, we already said that the higher the is, the higher the energy is. So we know that in equal six is higher and then we're going to a lower energy. So this must be the mission. We can then write the energy of the hotel. Honest energy difference. Years of interviews, energy of two. That's the energy level of six. And since we can't have a negative energy level of our focus on this is just the absolute value of the difference, or how we can also do. It is we know we just add another negative sign for emissions to get a positive energy at the end. So this becomes 13.6 e V, and then we have one over two squared minus one over C squared. What does that get us? Well, it gives us 3.0 electron balls. Look, part see says equals four, and we're moving to in prime Off again. We see in prime is bigger, so it's a higher energy level. So this leads us to absorption and we have energy of the proton is hated by the five minus four or negative acting coy. Six e V won over five squared minus one over four square. This one comes out to being even smaller interviews of 0.31 electron volts. So that means the 1st 1 or case A has our highest energy photons for the transition.


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