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Later,....people....realized....that....the....effect....was....caused....by....charge....screening,....with....an....inner....shell....containing....only....2....electrons.....This....was....established....empirically....before....Bohr....presented....his....model.....The..Bohr..model..gives..an..incorrect..value..L=..for..the..ground..state..orbital..angular..momentum:..The..angular..momentum..in..the..true..ground..state..is..known..to..be..zero..from..experiment.[8]..Although..mental..pictures..fail..somewhat..at..these..levels..of..scale,..an..electron..in..the..lowest..modern.."orbital"..with..no..orbital..momentum,..may..be..thought..of..as..not..to..rotate.."around"..the..nucleus..at..all,..but..merely..to..go..tightly..around..it..in..an..ellipse..with..zero..area..(this..may..be..pictured..as.."back..and..forth",..without..striking..or..interacting..with..the..nucleus)...It..also..determines..the..electron's..total..energy..at..any..radius:..E..=..1..2..m..e..v..2..−..Z..k..e..e..2..r..=..−..Z..k..e..e..2..2..r.....However,..these..numbers..are..very..nearly..the..same,..due..to..the..much..larger..mass..of..the..proton,..about..1836.1..times..the..mass..of..the..electron,..so..that..the..reduced..mass..in..the..system..is..the..mass..of..the..electron..multiplied..by..the..constant..1836.1/(1+1836.1)..=..0.99946...Electrons....can....only....gain....and....lose....energy....by....jumping....from....one....allowed....orbit....to....another,....absorbing....or....emitting....electromagnetic....radiation....with....a....frequency........determined....by....the....energy....difference....of....the....levels....according....to....the....Planck....relation:....Δ....E....=....E....2....−....E....1....=....h....ν........,....{displaystyle....Delta....{E}=E{2}-E{1}=hnu........,}....where....h....is....Planck's....constant.....(provides...an...elegant...reformulation...of...the...BohrSommerfeld...quantization...conditions,...as...well...as...an...important...insight...into...the...quantization...of...non-integrable...(chaotic)...dynamical...systems.).......Moseley's....law....and....calculation....of....K-alpha....X-ray....emission....lines[edit].....So...for...nuclei...with...Z...protons,...the...energy...levels...are...(to...a...rough...approximation):....

Calculation..of..the..orbits..requires..two..assumptions...Shell...model...of...heavier...atoms[edit]....Thirty...Years...That...Shook...Physics....New..York:..Dover..Publications...{displaystyle....nlambda....=2pi....r.}.........However,..this..is..not..to..say..that..the..Bohr..model..was..without..its..successes...Philosophical...Magazine....1913...in...science...Balmer's...Constant...Basic...concepts...of...quantum...mechanics...FranckHertz...experiment...provided...early...support...for...the...Bohr...model....Philosophical...Magazine....23,..2015...

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