University Physics Volume 3

# Key Equations

### Key Equations

 Orbital angular momentum $L=l(l+1)ℏL=l(l+1)ℏ$ z-component of orbital angular momentum $Lz=mℏLz=mℏ$ Radial probability density function $P(r)dr=|ψn00|24πr2drP(r)dr=|ψn00|24πr2dr$ Spin angular momentum $S=s(s+1)ℏS=s(s+1)ℏ$ z-component of spin angular momentum $Sz=msℏSz=msℏ$ Electron spin magnetic moment $μ→s=(eme)S→μ→s=(eme)S→$ Electron orbital magnetic dipole moment $μ→=−(e2me)L→μ→=−(e2me)L→$ Potential energy associated with the magneticinteraction between the orbital magnetic dipolemoment and an external magnetic field $B→B→$ $U(θ)=−μzB=mμBBU(θ)=−μzB=mμBB$ Maximum number of electrons in a subshell ofa hydrogen atom $N=4l+2N=4l+2$ Selection rule for atomic transitions in ahydrogen-like atom $Δl=±1Δl=±1$ Moseley’s law for X-ray production $(Z−1)=constantf(Z−1)=constantf$
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