# 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:

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

2. The radius of a nucleus:

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

3. Planck’s Quantum Theory:

$Energy\: of\: one\: photon = h v=\frac{ hc }{\lambda}$

4. Photoelectric Effect:

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

5. Bohr’s Model for Hydrogen like atoms:

• $mvr = n \frac{ h }{2 \pi}\: (Quantization\: of\: angular\: momentum)$
• $E _{ n }=-\frac{ E _{1}}{ n ^{2}} z ^{2}=2.178 \times 10^{-18} \frac{ z ^{2}}{ n ^{2}} J / atom =13.6 \frac{ z ^{2}}{ n ^{2}} eV ; \quad E _{1}=\frac{-2 \pi^{2} me ^{4}}{ n ^{2}}$
• $r_{n}=\frac{n^{2}}{z} \times \frac{n^{2}}{4 \pi^{2} e^{2} m}=\frac{0.529 \times n^{2}}{z} A$
• $v=\frac{2 \pi ze ^{2}}{ nh }=\frac{2.18 \times 10^{6} \times z }{ n } m / s$

6. De-Broglie wavelength:

$\lambda=\frac{ h }{ mc }=\frac{ h }{ p }(\text { for photon })$

7. Wavelength of emitted photon:

$\frac{1}{\lambda}=\bar{v}=R Z^{2}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)$

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

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

9. Heisenberg’s uncertainty principle:

$\Delta x . \Delta p>\frac{h}{4 \pi} or m \Delta x \cdot \Delta v \geq \frac{ h }{4 \pi}\: or\: \Delta x . \Delta v \geq \frac{h}{4 \pi m}$

10. Quantum Numbers:

• Principal quantum number $(n)=1,2,3,4 \ldots . . to\: \infty$
• Orbital angular momentum of electron in any orbit $=\frac{ nh }{2 \pi}$
• 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 = $\frac{ h }{2 \pi} \sqrt{\ell(\ell+1)}=\hbar \sqrt{\ell(\ell+1)}\left[\hbar=\frac{h}{2 \pi}\right]$