Important Atomic Structure Formulas for JEE Main and Advanced

Here students will find a list of all the important atomic structure formulas for JEE. Candidates can go through the formulas given here and revise quickly before the JEE Main or Advanced exam.

Atomic Structure Formulas

Find the detailed list of all the formulas of this chapter below.

1. Estimation of closest distance of approach (derivation) of α -particle:

R=4KZe2mαVα2R = \frac{4KZe^{2}}{m_{\alpha }V_{\alpha }^{2}}

2. The radius of a nucleus:

R=R0(A)1/3cm\quad R = R _{0}( A )^{1/3} cm

3. Planck’s Quantum Theory: 

Energyofonephoton=hv=hcλEnergy\: of\: one\: photon = h v=\frac{ hc }{\lambda}

4. Photoelectric Effect: 

hv=hv0+12mev2hv =h v_{0}+\frac{1}{2} m_{e} v^{2}

5. Bohr’s Model for Hydrogen like atoms:

  • mvr=nh2π(Quantizationofangularmomentum)mvr = n \frac{ h }{2 \pi}\: (Quantization\: of\: angular\: momentum)
  • En=E1n2z2=2.178×1018z2n2J/atom=13.6z2n2eV;E1=2π2me4n2E _{ n }=-\frac{ E _{1}}{ n ^{2}} z ^{2}=2.178 \times 10^{-18} \frac{ z ^{2}}{ n ^{2}} J / atom =13.6 \frac{ z ^{2}}{ n ^{2}} eV ; \quad E _{1}=\frac{-2 \pi^{2} me ^{4}}{ n ^{2}}
  • rn=n2z×n24π2e2m=0.529×n2zAr_{n}=\frac{n^{2}}{z} \times \frac{n^{2}}{4 \pi^{2} e^{2} m}=\frac{0.529 \times n^{2}}{z} A
  • v=2πze2nh=2.18×106×znm/sv=\frac{2 \pi ze ^{2}}{ nh }=\frac{2.18 \times 10^{6} \times z }{ n } m / s

6. De-Broglie wavelength: 

λ=hmc=hp( for photon )\lambda=\frac{ h }{ mc }=\frac{ h }{ p }(\text { for photon })

7. Wavelength of emitted photon:

1λ=vˉ=RZ2(1n121n22)\frac{1}{\lambda}=\bar{v}=R Z^{2}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)

8. Number of photons emitted by a sample of H atom: 

Δn(Δn+1)2\frac{\Delta n(\Delta n+1)}{2}

9. Heisenberg’s uncertainty principle:

Δx.Δp>h4πormΔxΔvh4πorΔx.Δvh4πm\Delta x . \Delta p>\frac{h}{4 \pi} or m \Delta x \cdot \Delta v \geq \frac{ h }{4 \pi}\: or\: \Delta x . \Delta v \geq \frac{h}{4 \pi m}

10. Quantum Numbers:

  • Principal quantum number (n)=1,2,3,,2,3,4 \ldots . . to\: \infty
  • Orbital angular momentum of electron in any orbit =nh2π=\frac{ nh }{2 \pi}
  • Azimuthal quantum number (l) = 0,1, …to (n-1)
  • Number of orbitals in a subshell = 2l + 1
  • Maximum number of electrons in particular subshell 2 x (2l + 1)
  • Orbital angular momentum L = h2π(+1)=(+1)[=h2π]\frac{ h }{2 \pi} \sqrt{\ell(\ell+1)}=\hbar \sqrt{\ell(\ell+1)}\left[\hbar=\frac{h}{2 \pi}\right]
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