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Natural Science Forum / Physics / Particle Physics / January 2006The Bohr Radius
The Bohr radius including the effect of reduced mass can be given by the following equation: a_0 = (lambda_p + lambda_e) / (2 * pi * alpha) where, lambda_p is the Compton wavelength of the proton. lambda_e is the Compton wavelength of the electron. alpha is the fine structure constant. In the above equation, the effect of the reduced mass is achieved by using the increased Compton wavelength, which is just the Compton wavelengths of the electron and the proton added together. Golden Boar a écrit : > The Bohr radius including the effect of reduced mass can be given by > the following equation: [quoted text clipped - 10 lines] > using the increased Compton wavelength, which is just the Compton > wavelengths of the electron and the proton added together. You equation gives 5.294654073E-11 m whereas the Bohr radius is 5.291772083E-11 m. Close, but not on the mark. André Michaud > Golden Boar a écrit : > > The Bohr radius including the effect of reduced mass can be given by [quoted text clipped - 18 lines] > > André Michaud The Bohr radius, a_0 = (hbar / m_e * c * alpha) http://en.wikipedia.org/wiki/Bohr_radius hbar = 1.05457168E-34 J s m_e = 9.1093826E-31 kg c = 299792458 m s^-1 alpha = 7.297352568E-3 this gives a value of 5.291772059E-11 for the Bohr radius, which is the same as your result of 5.291772083E-11. Both results should actually be 5.291772108E-11. This value is for the Bohr radius without taking into account the reduced mass of the electron and proton. The reduced mass is given by m_reduced = m_e * m_p / (m_e + m_p) Therefore, taking into account the recuced mass, the Bohr radius is, a_0 = hbar * (m_e + m_p) / (m_e * m_p * c * alpha) which is the same as, a_0 = (lambda_e + lambda_p) / (2 * pi * alpha) Golden Boar a écrit : >>Golden Boar a écrit : >> [quoted text clipped - 28 lines] > c = 299792458 m s^-1 > alpha = 7.297352568E-3 > this gives a value of 5.291772059E-11 for the Bohr radius, which is the > same as your result of 5.291772083E-11. Both results should actually be > 5.291772108E-11. Your constant values seem a little off with respect to CRC Handbook of Chemistry and Physics (2004 edition) Standard values on record: hbar = h/2pi = 1.054571596E-34 J s m_e = 9.10938188E-31 kg c = 299792458 m/s alpha = 7.297352533E-3 Which allows for your last equation for the Bohr radius a_0 = (hbar / m_e c alpha) = 5.291772081E-11 m If you want easily obtained precise calculations from fundamental constants, there are inexpensive "scientific" pocket calculators that have most of them stored as constants in memory. Their constants are precise and are an exact match to NIST standard and CRC Handbook (which has the same sources) The one I regularly use is a simple $20.00 CASIO fx-991MS > This value is for the Bohr radius without taking into account the > reduced mass of the electron and proton. [quoted text clipped - 10 lines] > > a_0 = (lambda_e + lambda_p) / (2 * pi * alpha) I wonder to what use you would want to put such a revised value of a_0. André Michaud > Golden Boar a écrit : > > [quoted text clipped - 77 lines] > > André Michaud The values that I gave for the constants were taken directly from the NIST website, so the ones in your book are slightly off. What use would such a revised value have? Well it would give the correct results for a start. and what shell we do in case that there is not even a single case in which an atom is a ;sphere?? (:-) shell we say that we are wasting our precious time?? ATB Y.Porat ------------------ shell -> shall How does that "reduced mass" work? Wat do you mean by "How does that "reduced mass" work?" > Wat do you mean by "How does that "reduced mass" work?" What does that expression do? It gives the value of the Bohr radius. The Bohr radius excluding effect of reduced mass is, a0 = rCe / alpha The Bohr radius including effect of reduced mass is, a0 = (rCe+rCp) / alpha > It gives the value of the Bohr radius. > > The Bohr radius excluding effect of reduced mass is, a0 = rCe / alpha > The Bohr radius including effect of reduced mass is, a0 = (rCe+rCp) / > alpha I forgot to add that, rCe is the electron Compton wavelength over 2pi rCp is the proton Compton wavelength over 2pi you didnt answer my question: what will happen with your 'radius' once it will be found that there is not even a single atom that is spheric shell we say then that you are playing just your mathematics chess with yourself? and some parrots or shell we say that it is just a course approximation?-- that prevents better understanding of the Atom??. ATB Y.Porat --------------- First of all, the reply you gave was to srp, not me. Secondly, it it not 'my' radius, it is Bohr's radius. Thirdly, if the electron was in a stable orbit around the nucleus, I believe the orbit would be ellipticcal, not circular. Fourthly, the Bohr model is an outdated model, so i guess you could say that it is just an approximation. P.S. I disagree with your 'no mass, no physics' argument. By replacing any mass terms in an equation with either energy or Compton wavelength or both, the equation is usually simplified, as shown above. Mass is just something like the resistance of an energy packet to changes in its spacetime co-ordinates. Instead of asking why an electron has the mass it does, we should be asking why it has the Compton wavelength that it does, although they are basicaly the same thing. Mass is inversely proportional to the Compton wavelength, the constant of proportionality being Planck's constant divided by the speed of light, h / c. I prefer using the Compton wavelength over 2pi though, as this is equivalent to the Planck length. > First of all, the reply you gave was to srp, not me. > Secondly, it it not 'my' radius, it is Bohr's radius. > Thirdly, if the electron was in a stable orbit around the nucleus, I > believe the orbit would be ellipticcal, not circular. > Fourthly, the Bohr model is an outdated model, so i guess you could say > that it is just an approximation. fiftly we agree about the above but you ddint notice my important remark that dealing with an 'atm radius' is harmful for more advance !! for instance somenews for you : all atoms from Fluorine upwards are sort of 'rectangula pipes' or more acurately octangular pipes 2 all atoms have more or less the same volume!!! (a big surprise for many people) see my model at http://www.geocities.com/porat_y/mypage.html the size of atoms can be derived and concluded from tables no 2 and 3 there )if you are smart enough and open minded) > P.S. I disagree with your 'no mass, no physics' argument. i am very happy that you and others disagree or else...... or else it would not be so revolutionary and innovative (:-) and imporatnt and powefully simply!! By replacing > any mass terms in an equation with either energy or Compton wavelength > or both, the equation is usually simplified, as shown above. > Mass is just something like the resistance of an energy packet to > changes in its spacetime co-ordinates. wrong there is mass even without energy!! if mass is in rest! so mass is much more fendamental than your Compton wavelengths. and if you dont mind energy is exactly as in macrocosm: mass in motion!! so please a bit much more respect to one of the most fundamental physical entities that is called mass. --------- > Instead of asking why an electron has the mass it does, we should be > asking why it has the Compton wavelength that it does, a strange approach the electron has a wavelength only if it is in motion if not --- it does not so what is a more basic definition mass of wavelength?? i start to suspect that you belong to some company that deals with waves ???or may be even makes its living form that ?? ------- although they > are basicaly the same thing. Mass is inversely proportional to the > Compton wavelength, mass was discovered much earlier than the cpmpton wave length and belongs to much more physical entities than waves so ???!!! (did you do your Phd on Compton .......) the constant of proportionality being Planck's > constant divided by the speed of light, h / c. I prefer using the > Compton wavelength over 2pi though, as this is equivalent to the Planck > length. as i said mass belongs to much more physical entlties that has nothing to do with waves so your argunets is atrange (just myhumble oppinion) (i hope you will present the above oppinions of yours as just your humble oppinions --excluding the ones we agreed upon) ATB Y.Porat ----------------------------- > > First of all, the reply you gave was to srp, not me. > > Secondly, it it not 'my' radius, it is Bohr's radius. [quoted text clipped - 7 lines] > but you ddint notice my important remark that dealing with > an 'atm radius' is harmful for more advance !! I was commenting more on the fact that it easier to use the increased Compton wavelength than it is to use the reduced mass in this equation. > for instance somenews for you : > [quoted text clipped - 11 lines] > there > )if you are smart enough and open minded) I'm very open minded, though I don't know about smart enough :) I checked out your site, but it was too painful on the eyes, it needs a lot of cleaning up! I suggest you use some type of drawing or modelling software. > > P.S. I disagree with your 'no mass, no physics' argument. > [quoted text clipped - 14 lines] > energy is exactly as in macrocosm: > mass in motion!! Think about it logically. Can you tell me one thing that is at absolute rest? Nope, didn't think so! If nothing is at rest, then how can you have rest mass or even rest energy for that matter? This fits in nicely with special relativity as follows: Nothing can be accelerated to the speed of light, or be deccelerated to an absolute rest in a vacuum. > so please a bit much more respect to one of the most fundamental > physical entities that is called mass. That little con artist has been conning us too long, he pulled a reverse 'Keyser Soze' on us. > --------- > > Instead of asking why an electron has the mass it does, we should be [quoted text clipped - 4 lines] > if not --- it does not > so what is a more basic definition mass of wavelength?? You are confusing the Compton wavelength with the de Broglie wavelength. The classical electron circumference, which can be thought of as the size of the electron, is the electron Compton wavelength multiplied by the fine structure constant. The Compton wavelength sets the cross-section of interactions, so I would say this is the more fundamental definition. > i start to suspect that you belong to some company > that deals with waves ???or may be even makes its living form that ?? > ------- Nope, I'm currently unemployed. > although they > > are basicaly the same thing. Mass is inversely proportional to the [quoted text clipped - 3 lines] > and belongs to much more physical entities than waves > so ???!!! Science progresses. > (did you do your Phd on Compton .......) I don't have a PhD. > the constant of proportionality being Planck's > > constant divided by the speed of light, h / c. I prefer using the [quoted text clipped - 3 lines] > as i said mass belongs to much more physical entlties > that has nothing to do with waves You said it. Mass 'belongs' to physical entities. It is a property of energy which causes energy to resist changes in its space-time co-ordinates. There is nothing physical about mass, for example, you cannot touch mass. > so your argunets is atrange (just myhumble oppinion) > (i hope you will present the above oppinions of yours as just > your humble oppinions --excluding the ones we agreed upon) I hope I explained my strange arguments well enough. :) Some of the arguments above are just my opinions, some are scientific facts. > > > First of all, the reply you gave was to srp, not me. > > > Secondly, it it not 'my' radius, it is Bohr's radius. [quoted text clipped - 10 lines] > I was commenting more on the fact that it easier to use the increased > Compton wavelength than it is to use the reduced mass in this equation. if you take an atom in a matal latice does it have a wavelenth?? it certainly has mass that you can determine without any wavelenth!! and it is in rest. > > for instance somenews for you : > > [quoted text clipped - 15 lines] > I checked out your site, but it was too painful on the eyes, it needs a > lot of cleaning up! indeed a lot of cleam up but not of itys substance: for instance have a look at my tables 2 and 3 i will help you if it is too mysterious for you: it showes that a small atom like Aluminum has more or less the same volume !!!!! is it not a surprise for you and others that talk about 'atom radius ' ?? you see there that for instance; Aluminum Argentum and Gold havemore or less the same volume in a matal latice!! how come with all those electrons shells ?? does your Compton wavelength show it ?? ------------ > I suggest you use some type of drawing or modelling software. my be i am just a poor amature in site building but that shoud not diminish the importance of its substance (for cleaver and honest prople only !! ) ------------- > > > P.S. I disagree with your 'no mass, no physics' argument. > > [quoted text clipped - 18 lines] > Can you tell me one thing that is at absolute rest? > Nope, didn't think so! why not the chair you sit on it is in reast why all the big phylosophysing about it?? ---------- > If nothing is at rest, then how can you have rest mass or even rest > energy for that matter? so according to you there i sno rest mass at all ?? you have to demand a copyright on it ! -------------- > This fits in nicely with special relativity as follows: > > Nothing can be accelerated to the speed of light, or be deccelerated to > an absolute rest in a vacuum. the photon (that has mass) can move at the speed of light it cannot be accelerated because its velocity is constant and the maximun veleocity and nothiong is moving faster so nothing can accelerate it!! complicated ??!! ------------- > > so please a bit much more respect to one of the most fundamental > > physical entities that is called mass. > > That little con artist has been conning us too long, he pulled a > reverse 'Keyser Soze' on us. ????? > > --------- > > > Instead of asking why an electron has the mass it does, we should be [quoted text clipped - 7 lines] > You are confusing the Compton wavelength with the de Broglie > wavelength. the electron is not orbiting around the Atom so De berglie trheory seens to be of dated. > The classical electron circumference, which can be thought of as the > size of the electron, is the electron Compton wavelength multiplied by > the fine structure constant. that is mathemethics not he physical reality > The Compton wavelength sets the cross-section of interactions, so I > would say this is the more fundamental definition. as before - it ios not reality it is a mathematical model only!! > > mass was discovered much earlier than the cpmpton wave length > > and belongs to much more physical entities than waves > > so ???!!! > > Science progresses. not anything that is 'new' can replace the older substantiated theory 2 not anything new is vast enough to include everthing in physics. iow not everything new is relevant to all physics aspects! the Compton wavelength is a goo sexample to that you remind me the man that has a big hammer in his hands so while he goes out anything on the street looks to him like - nails !! ------------------ ATB Y.Porat ---------------------- > > > > First of all, the reply you gave was to srp, not me. > > > > Secondly, it it not 'my' radius, it is Bohr's radius. [quoted text clipped - 13 lines] > if you take an atom in a matal latice > does it have a wavelenth?? It certainly does. > it certainly has mass that you can determine without any wavelenth!! > and it is in rest. It most certainly is not at rest. The atoms in a condensate are not even at rest, never mind in a solid. > > > for instance somenews for you : > > > [quoted text clipped - 26 lines] > is it not a surprise for you and others that talk about 'atom radius ' > ?? Considering the sizes of electrons and protons compared to atoms, it would not surprise me. > you see there that for instance; > > Aluminum Argentum and Gold > havemore or less the same volume in a matal latice!! > how come with all those electrons shells ?? An atom is about 100,000,000 times bigger than an electron. > does your Compton wavelength show it ?? It is not 'my' Compton wavelength, it is "Compton's" wavelength. If mass shows it, then so can the Compton wavelength. > ------------ > > I suggest you use some type of drawing or modelling software. [quoted text clipped - 30 lines] > the chair you sit on it is in reast > why all the big phylosophysing about it?? The chair I sit on is not at rest. The chair is located on the Earth, the Earth is rotating around itself, it is also rotating around the sun. The sun is going around the galaxy, and even the galaxy is moving. > ---------- > > > > If nothing is at rest, then how can you have rest mass or even rest > > energy for that matter? > > so according to you there i sno rest mass at all ?? Exactly! No rest for the wicked :) > you have to demand a copyright on it ! > -------------- [quoted text clipped - 11 lines] > complicated ??!! > ------------- Exactly my point, photons cannot be accelerated. > > > so please a bit much more respect to one of the most fundamental > > > physical entities that is called mass. [quoted text clipped - 3 lines] > > ????? I guess you have never seen the film 'The Usual suspects', it's an excellent movie. Here's a quote from the film. "The greatest trick the devil ever pulled, was to convince the world that he didn't exist." So what I meant was that the greatest trick that mass pulled, was to convince the world that it does exist. > > > --------- > > > > Instead of asking why an electron has the mass it does, we should be [quoted text clipped - 10 lines] > the electron is not orbiting around the Atom > so De berglie trheory seens to be of dated. But things do have wavelengths. > > The classical electron circumference, which can be thought of as the > > size of the electron, is the electron Compton wavelength multiplied by [quoted text clipped - 6 lines] > > as before - it ios not reality it is a mathematical model only!! So, Thomson scattering is not real then? > > > mass was discovered much earlier than the cpmpton wave length > > > and belongs to much more physical entities than waves [quoted text clipped - 16 lines] > Y.Porat > ---------------------- Bye i am wasting my precious time. Y.Porat ----------------------- As c is variable for different media and universal eras, fotons can be accelerate in scalar and vector means. > First of all, the reply you gave was to srp, not me. > Secondly, it it not 'my' radius, it is Bohr's radius. > Thirdly, if the electron was in a stable orbit around the nucleus, I > believe the orbit would be ellipticcal, not circular. > Fourthly, the Bohr model is an outdated model, so i guess you could say > that it is just an approximation. fiftly we agree untill now btw i was replying but it doe snot show so i have to do it again:: > P.S. I disagree with your 'no mass, no physics' argument. i am happy that you dont agree or else my achievement would not be obvious or trivial. By replacing > any mass terms in an equation with either energy or Compton wavelength > or both, the equation is usually simplified, as shown above. > Mass is just something like the resistance of an energy packet to > changes in its spacetime co-ordinates. curved space time is one of Eisteins faliurs. 2 mass is existing in too many phisical entities that have nothing to do with waves. wavelength is only in motion while mass exists even wothout motion so waht is more basic ?? if you dont mind energy is *mass in motion* exactly as in macrocosm there is no justification to change it arbitrarily in microcosm just to satisfy some theory or wrong interpretations of a theory. ------------ > Instead of asking why an electron has the mass it does, we should be > asking why it has the Compton wavelength that it does, even the electron has situations of mass without anywaves pruduction. -------- although they > are basicaly the same thing. Mass is inversely proportional to the > Compton wavelength, the constant of proportionality being Planck's > constant divided by the speed of light, h / c. I prefer using the > Compton wavelength over 2pi though, as this is equivalent to the Planck > length. ---------------------- mass was discovered much before any Plank constant and exists in physical phenonena that has nothing to do with waves. -------- some news for you: all atoms above Fluorine are actually like a rectangular pipe not sperically at all if you have a single Atom that ritates like in Gas it lokks only as spherical 2 all Atoms are more or less the same volume!! would you believe that?? if not see my table 2 and 3 in my site: http://www.geocities.com/porat_y/mypage.html and you have some some shocking news. ATB Y.Porat ------------------------- Dammit, stray charge wonked up my trackpad, and made one click into 16. That would be useful for other steads, if I could replicate it. I blew the wristrest to get dust off, and it happened. But now my breath is damp as I took a Pepsi. -Aut > Dammit, stray charge wonked up my trackpad, and made one click into 16. > That would be useful for other steads, if I could replicate it. I > blew the wristrest to get dust off, and it happened. But now my breath > is damp as I took a Pepsi. Did you remember to take your tablets with the pepsi?  Signaturerusty shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? shell -> shall How does that "reduced mass" work? |
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