Important Atomic Structure Formulas For JEE For Quick Revision

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.

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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:

\(\begin{array}{l}R = \frac{4KZe^{2}}{m_{\alpha }V_{\alpha }^{2}}\end{array} \)

2. The radius of a nucleus:

\(\begin{array}{l}\quad R = R _{0}( A )^{1/3} cm\end{array} \)

3. Planck’s Quantum Theory:

\(\begin{array}{l}Energy\: of\: one\: photon = h v=\frac{ hc }{\lambda}\end{array} \)

4. Photoelectric Effect:

\(\begin{array}{l}hv =h v_{0}+\frac{1}{2} m_{e} v^{2}\end{array} \)

5. Bohr’s Model for Hydrogen like atoms:

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

6. De-Broglie wavelength:

\(\begin{array}{l}\lambda=\frac{ h }{ mc }=\frac{ h }{ p }(\text { for photon })\end{array} \)

7. Wavelength of emitted photon:

\(\begin{array}{l}\frac{1}{\lambda}=\bar{v}=R Z^{2}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)\end{array} \)

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

\(\begin{array}{l}\frac{\Delta n(\Delta n+1)}{2}\end{array} \)

9. Heisenberg’s uncertainty principle:

\(\begin{array}{l}\Delta x . \Delta p>\frac{h}{4 \pi} or m \Delta x \cdot \Delta v \geq \frac{ h }{4 \pi}\: or\: \Delta x . \Delta v \geq \frac{h}{4 \pi m}\end{array} \)

10. Quantum Numbers:

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