Answer: Find Wavelength of H-atom Induced Radiation

[Saitama]

PLEASE: Minimum wavelength = maximum energy !

Maximum emitted energy = incoming energy

i thought you had confirmed both those facts earlier ??

EDIT: Have you realized that Option (a) is the nanometre equivalent of the Angstrom Unit wavelength of the incoming radiation?

Yes i have confirmed those facts.
And yes i have realized that option (a) is the nm equivalent of the Angstrom Unit wavelength of the incoming radiation.

Can you be a little bit more expansive please?
Provide a little more detail about what you do not get?
And perhaps on what you do get?

I don't get why we checked the wavelength when transition takes place between 1st level and 2nd level and between 1st level and 3rd level. And when we found the matching wavelength, we stopped at third level and we didn't proceed further to the fourth level.

 

[PeterO]

Yes i have confirmed those facts.
And yes i have realized that option (a) is the nm equivalent of the Angstrom Unit wavelength of the incoming radiation.



I don't get why we checked the wavelength when transition takes place between 1st level and 2nd level and between 1st level and 3rd level. And when we found the matching wavelength, we stopped at third level and we didn't proceed further to the fourth level.

I can't understand why you are checking any levels at all. Decay from any excited level will be either the same as the incoming radiation [one big drop] or SMALLER - several smaller drops.
You are trying to find the biggest drop.

 

[Saitama]

I can't understand why you are checking any levels at all. Decay from any excited level will be either the same as the incoming radiation [one big drop] or SMALLER - several smaller drops.
You are trying to find the biggest drop.

I too don't understand why i was made to check for the levels?

 

[PeterO]

Homework Statement

H-atom is exposed to electromagnetic radiation of $\lambda$=1025.6 $\dot{A}$ and excited atom gives out induced radiations. What is the minimum wavelength of these induced radiation:
(a)102.6 nm
(b)12.09 nm
(c)121.6 nm
(d)810.8 nm

Just in case you have forgotten the original question.

The two words I highlighted confirmed that the H-Atom was excited to a higher level, so the incoming radiation had an energy matching one of the excited levels.

The decay back to ground state will be either in one big jump - straight back to ground state - or a series of cascades via lower levels, if there are any.

The minimum wavelength of induced radiation corresponds to the largest energy given off.

The largest energy of induced radiation is from the single, big jump. That energy is the same as the incoming radiation.

So the answer is the same wavelength as the incoming - the nm version of the Angstoms.

Peter

 

[PeterO]

I too don't understand why i was made to check for the levels?

I didn't realize you felt someone made you check the levels? Certainly I never did. On the contrary I repeatedly said it was unnecessary.

EDIT: But you repeatedly claimed you didn't get why option (a) was the minimum wavelength !??

 

[Saitama]

Just in case you have forgotten the original question.

The two words I highlighted confirmed that the H-Atom was excited to a higher level, so the incoming radiation had an energy matching one of the excited levels.

The decay back to ground state will be either in one big jump - straight back to ground state - or a series of cascades via lower levels, if there are any.

The minimum wavelength of induced radiation corresponds to the largest energy given off.

The largest energy of induced radiation is from the single, big jump. That energy is the same as the incoming radiation.

So the answer is the same wavelength as the incoming - the nm version of the Angstoms.

Peter

Oh Wow! Thank you so much! I got it now!

(Sorry for irritating you and ILS for such an easy question. )

 

[I like Serena]

I don't get why we checked the wavelength when transition takes place between 1st level and 2nd level and between 1st level and 3rd level. And when we found the matching wavelength, we stopped at third level and we didn't proceed further to the fourth level.

The transition does not take place between 1st and 2nd level, since the energy signature does not match.
We stopped at 3rd level, since we found a match in the energy signature, so there was no point in continuing to the 4th level.

Ultimately the point of doing the question, and perhaps doing a little more work than necessary, is to get an understanding of how the atom, excitation, absorption, emission, and quantum states work.
Do you feel you have learned something? And that you can do more questions like this one?

 

[Saitama]

The transition does not take place between 1st and 2nd level, since the energy signature does not match.
We stopped at 3rd level, since we found a match in the energy signature, so there was no point in continuing to the 4th level.

Ultimately the point of doing the question, and perhaps doing a little more work than necessary, is to get an understanding of how the atom, excitation, absorption, emission, and quantum states work.
Do you feel you have learned something? And that you can do more questions like this one?

Yes, i think i have learned a lot from this discussion but still one question arises in my mind.
What would happen if there was no energy match? How then we would find out the minimum wavelength of the induced radiation?

 

[I like Serena]

What would happen if there was no energy match? How then we would find out the minimum wavelength of the induced radiation?

Then the photon would not be absorbed and there would be no induced radiation.

 

[Saitama]

Why the photon won't be absorbed?

 

[I like Serena]

Why the photon won't be absorbed?

Dunno. ;)
Experiments done by great scientists say so.
That's why it's called "quantum" physics.
Energy can only exist and be transferred in a specific "quantum".

 

[Saitama]

Dunno. ;)
Experiments done by great scientists say so.
That's why it's called "quantum" physics.
Energy can only exist and be transferred in a specific "quantum".

Thanks for your explanation!

 

[PeterO]

Why the photon won't be absorbed?

For photon to be absorbed, it has to be an exact energy match.

If the incoming "radiation" had been a stream of electrons - particles - then they could collide and pass on part of their energy only [not unlike a pair of billard balls colliding].

With photons, they either pass on ALL their energy or NONE of their energy.

[and the underlying principle is that the atom can only accept specific discrete amounts of energy]

EDIT: The energy of a photon is related to its frequency [or wavelength]. The frequency is determined by the source of the radiation. If the photon later interacts with an atom it is either absorbed totally, or scattered without energy loss. The collision cannot change the frequency of the radiation - so cannot take part of the photon energy.

 

[anshul arora]

when electron exite from a particular state to another stae by absorbing energy, then the electron tries to return to the orginal exited state and if possible to the ground state. these radiations that are emitted by the electron to return back to the ground state are called induced radiations.

in this questions energy supplied to the hydrogen atom is 12400/1028 ev = 12.06ev.

(note- energy gap between two shells is 12.06 ev hence electron will exite from ground state.
this is because energy is 2nd shell of hydorgen atom is -3.4ev and energy of elctron at ∞ is 0 then if electron would have have excited from 2nd energy level then max energy level would be 3.4 and would never reach 12.06 ev)

energy of electon at excited energy level = -13.6-(-12.06)ev = -1.54ev

calculating n, -1.54 = -13.6*z²/n² (where z=1)
gives n = 3

therefore, electrons can transist to all below possible energy level to produce all possible photons.
3→1
3→2
2→1
solving for λ, you will observe that the minimum wavelength is observed when electron will transist from 3 to 1 which is equal to 102.6 nm

 

[anshul arora]

answer is (a)