Physics - Ch 66.5 Quantum Mechanics: The Hydrogen Atom (41 of 78) What is the Reduced Mass?

[@phoenixelectronics2631]

Thanks Sir.. From last 3-4 days I was struck in a problem of atomic structure which includes this Reduse Mass concept.. You cleared my all doubts. Thanks a lot.❤

[@wadalupe1900]

best video I've found to understand the concept.

[@MichelvanBiezen]

Glad you found our videos.

[@SaebaRyo21]

Thank you very much for such a great explanation; I had been confused for long about this topic.

[@matricmasterclass4245]

Hi Michel can you please explain in 3:38 how you got that the E = p^2/2mR. Is it because we assume the momentum of the proton is zero which means that: Et = 0 + p^2/m where m = mass of electron. but since we made the proton have zero momentum, the mass of the electron would have to change and we therefore represent it as "mR"? Thanks :)

[@MichelvanBiezen]

Mr represents the "reduced mass" and is defined as: Mr = m M / (m + M)

[@ganquan4419]

Thank u, saved my life

[@MichelvanBiezen]

Glad we were able to help. (We know the feeling, we were students once desparate trying to find material that could help us understand).

[@angelomertr1686]

exactly what I needed, thanks :)

[@MichelvanBiezen]

Glad you found us.

[@ayyanarvenkat9304]

Thanks a lot sir for this clear explanation which i was searching for..

[@MichelvanBiezen]

Happy to help

[@pratikshabairagi6391]

Thank you sir... I really understood well ... But it is a bit unfortunate that i found you video after being stressed out after watching a lots of videos from hours on this topic and no one was relevent for me.

[@MichelvanBiezen]

That is too bad. At least you have found us now. Yes, you will not find the needed details in very many places. That is why we started making the videos in the first place.

[@Vanilliana1004]

Sir how can i determination of reduced mass of atom by effect of velocity

[@MichelvanBiezen]

The reduced mass would only be affected by velocity if the speeds were relativistic.

[@soumikchakraborty9885]

so sir , protron is also moving about canter of mass just like gravitational sysytem ? is it right sir ?

[@soumikchakraborty9885]

please reply

[@MichelvanBiezen]

Due to the quantum mechanic effects, the proton in a hydrogen atom does not move around the barycenter as in the Earth-Moon system or the Sun-Earth system.

[@soumikchakraborty9885]

@@MichelvanBiezen so why you describe this in this approach.please answer.

[@MichelvanBiezen]

It is a good approximation if we consider the Bohr model of the atom. From that perspective, the model with the barycenter is correct.

[@soumikchakraborty9885]

@@MichelvanBiezen sir , what you mean "model with barycenter "?

[@magn8195]

When working out the reduced mass for a helium atom do I consider the two electrons?

[@MichelvanBiezen]

No, we don't include the electrons.

[@soumikchakraborty9885]

@@MichelvanBiezen why sir ,please reply ?

[@aryensujjan]

Excellent

[@MichelvanBiezen]

Thank you. 🙂

[@adosar7261]

So we fix our reference frame in the proton ? But why you assume that center of mass isn't moving ? Thanks in advantage.

[@MichelvanBiezen]

The reference frame is the center of mass, not the proton. It is the same for the Moon and the Earth. When the Moon revolves around the Earth, the Earth makes little circles around the center of mass (known as the barycenter)

[@adosar7261]

If we fix our reference frame in center of mass then where the proton goes ? We consider only the motion of 1 body with the reduced mass ? could the particle with the reduced mass be the more massive ? Sorry for too many questions.

[@MichelvanBiezen]

Take a look at this video. It may help you to understand. Astrophysics: Binary Star System (8 of 40) The Barycenter: A General Approach

[@IshanChaudharii]

Wow ! I just understood it in first go 😯I was so confused about it ...thank you so much sir 😇💝

[@MichelvanBiezen]

Most welcome 😊

[@rasikaprabhu8583]

Sir, what is effect of reduced mass on Rydberg constant?

[@MichelvanBiezen]

There is a theoretical value for the Rydberg constant. But the value to be used for each atom does depend on the reduced mass, which has the effect of making the value of the Rydberg constant for each atom a bit smaller than the theoretical value.

[@rasikaprabhu8583]

@@MichelvanBiezen sir, what about two isotopes, say hydrogen and deuterium , who will have smaller value of R ? And why?

[@MichelvanBiezen]

The factor for the reduced Rydberg constant is: 1/(1 + (m/M)) m = mass of the electron and M = mass of the nucleus Thus the larger the nucleus the closer the reduced Rydberg constant will be to the theoretical value where M approaches infinity

[@rasikaprabhu8583]

@@MichelvanBiezen thank you sir

[@sibusisomaseko1607]

What about compensating for relativistic mass? Or is this ignorable

[@MichelvanBiezen]

At the speed of the electrons in the atom, we can ignore it.

[@iamnoob4232]

why neutron didn't have Ek too?? did neutron didn,t move cause it is netral??

[@MichelvanBiezen]

When an atom containing neutrons moves, the neutron, just like the proton has kinetic energy. (A hydrogen atom does not contain a neutron).

[@iamnoob4232]

@@MichelvanBiezen i see, so for case another atom ( not hydrogen atom), We have to add Mneutron for mass reduce. Mr= { (Mn + Mp) Me }/{(Mn + Mp)+ Me} This is correct sir? For another atom ( not hydrogen atom) have

[@MichelvanBiezen]

That is correct, you need to account for the mass of the neutrons in other atoms.

[@iamnoob4232]

@@MichelvanBiezen i understand now sir. Thanks for your knowledge 😊😊😊

[@아니한빈아]

How can we talk about 'P = p'?? because of little M & m?

[@MichelvanBiezen]

Yes, that is the notation I use to recognize the 2 particles. M, P for the large particle. m, p for the small particle

[@efetaluerdener7342]

Thank you.

[@MichelvanBiezen]

You're welcome!

[@MinMax-kc8uj]

I'm thinking the electron and proton do that retrograde motion thing when traveling through time. And the loop does not stay in the same place when looking down the barrel. So, the whole space would fill up and it would look like a cylinder with a wall, if you were able to time travel, that is. Also, m and M kind of looks like that math they do with resistor ladders. It's recursive, Fib[2n]/Fib[2n-1]. I think it's a squared q-matrix. If it is, it's generalizable. The contour map has a magnetic field look but has a swirl. The poles are phi and -1/phi. I'm not a mathematician, or a physics guy. Just a floor layer that's mildly interested in Fibonacci Numbers.

[@congminhang3339]

Sorry, but why P equal p ? Masses of Proton and Electron are different and so are their speed !?

[@arya7004]

the velocity of the centre of mass is zero, therefore the momenta of the two species constituting the system is equal and opposite

[@congminhang3339]

@@arya7004 Is it the law of conservation of momentum?

[@MichelvanBiezen]

The mass of the proton is about 1836 times the mass of the electron.

[@nithin1729s]

Sir, can i use this concept in Mechanics too. Is it confined only to quantum mechanics???

[@jameelahmad7923]

Yes, you can. In fact, it is actually confined to classical mechanics! To use it in quantum mechanics, we have to make the assumption that the electron is orbiting the nucleus in a defined circle, which is not the case.

[@sameermalviya9882]

Thank u soo much sir

[@MichelvanBiezen]

Most welcome

[@Priya-ps8mo]

Thank u sir!

[@MichelvanBiezen]

Most welcome!

[@nithin1729s]

Any Jee adv aspirants

[@ssurajbadrinarayanan7999]

Yes

[@arjunprasad3535]

Neet aspirant!

[@anhquocnguyen1967]

Thank you so much

[@MichelvanBiezen]

You're most welcome

[@udithkumarv734]

❤