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{4 K Z e^{2}}{m_{α} V_{α}^{2}} \end{array}

2. The radius of a nucleus:

\begin{array}{l} R = R_{0} (A)^{1 / 3} c m \end{array}

3. Planck’s Quantum Theory:

\begin{array}{l} E n e r g y o f o n e p h o t o n = h v = \frac{h c}{λ} \end{array}

4. Photoelectric Effect:

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

5. Bohr’s Model for Hydrogen like atoms:

$\begin{array}{l} m v r = n \frac{h}{2 π} (Q u a n t i z a t i o n o f a n g u l a r m o m e n t u m) \end{array}$
$\begin{array}{l} E_{n} = - \frac{E_{1}}{n^{2}} z^{2} = 2.178 \times 10^{- 18} \frac{z^{2}}{n^{2}} J / a t o m = 13.6 \frac{z^{2}}{n^{2}} e V; E_{1} = \frac{- 2 π^{2} m e^{4}}{n^{2}} \end{array}$
$\begin{array}{l} r_{n} = \frac{n^{2}}{z} \times \frac{n^{2}}{4 π^{2} e^{2} m} = \frac{0.529 \times n^{2}}{z} A \end{array}$
$\begin{array}{l} v = \frac{2 π z e^{2}}{n h} = \frac{2.18 \times 10^{6} \times z}{n} m / s \end{array}$

6. De-Broglie wavelength:

\begin{array}{l} λ = \frac{h}{m c} = \frac{h}{p} (for photon) \end{array}

7. Wavelength of emitted photon:

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

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

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

9. Heisenberg’s uncertainty principle:

\begin{array}{l} Δ x . Δ p > \frac{h}{4 π} o r m Δ x \cdot Δ v \geq \frac{h}{4 π} o r Δ x . Δ v \geq \frac{h}{4 π m} \end{array}

10. Quantum Numbers:

Principal quantum number
$\begin{array}{l} (n) = 1, 2, 3, 4 \dots . . t o \infty \end{array}$
Orbital angular momentum of electron in any orbit
$\begin{array}{l} = \frac{n h}{2 π} \end{array}$
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 =
$\begin{array}{l} \frac{h}{2 π} \sqrt{ℓ (ℓ + 1)} = ℏ \sqrt{ℓ (ℓ + 1)} [ℏ = \frac{h}{2 π}] \end{array}$

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Atomic Structure Formulas

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Structure of Atom

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