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 = 4 K Z e 2 m α V α 2 R = \frac{4KZe^{2}}{m_{\alpha }V_{\alpha }^{2}} R = m α V α 2 4 K Z e 2 2. The radius of a nucleus:
R = R 0 ( A ) 1 / 3 c m \quad R = R _{0}( A )^{1/3} cm R = R 0 ( A ) 1 / 3 c m
3. Planck’s Quantum Theory:
E n e r g y o f o n e p h o t o n = h v = h c λ Energy\: of\: one\: photon = h v=\frac{ hc }{\lambda} E n e r g y o f o n e p h o t o n = h v = λ h c
4. Photoelectric Effect:
h v = h v 0 + 1 2 m e v 2 hv =h v_{0}+\frac{1}{2} m_{e} v^{2} h v = h v 0 + 2 1 m e v 2
5. Bohr’s Model for Hydrogen like atoms:
m v r = n 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 ) mvr = n \frac{ h }{2 \pi}\: (Quantization\: of\: angular\: momentum) m v r = n 2 π h ( 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 ) E n = − E 1 n 2 z 2 = 2.178 × 1 0 − 18 z 2 n 2 J / a t o m = 13.6 z 2 n 2 e V ; E 1 = − 2 π 2 m e 4 n 2 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}} E n = − n 2 E 1 z 2 = 2 . 1 7 8 × 1 0 − 1 8 n 2 z 2 J / a t o m = 1 3 . 6 n 2 z 2 e V ; E 1 = n 2 − 2 π 2 m e 4 r n = n 2 z × n 2 4 π 2 e 2 m = 0.529 × n 2 z A r_{n}=\frac{n^{2}}{z} \times \frac{n^{2}}{4 \pi^{2} e^{2} m}=\frac{0.529 \times n^{2}}{z} A r n = z n 2 × 4 π 2 e 2 m n 2 = z 0 . 5 2 9 × n 2 A v = 2 π z e 2 n h = 2.18 × 1 0 6 × z n m / s v=\frac{2 \pi ze ^{2}}{ nh }=\frac{2.18 \times 10^{6} \times z }{ n } m / s v = n h 2 π z e 2 = n 2 . 1 8 × 1 0 6 × z m / s
6. De-Broglie wavelength:
λ = h m c = h p ( for photon ) \lambda=\frac{ h }{ mc }=\frac{ h }{ p }(\text { for photon }) λ = m c h = p h ( for photon )
7. Wavelength of emitted photon:
1 λ = v ˉ = R Z 2 ( 1 n 1 2 − 1 n 2 2 ) \frac{1}{\lambda}=\bar{v}=R Z^{2}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right) λ 1 = v ˉ = R Z 2 ( n 1 2 1 − n 2 2 1 )
8. Number of photons emitted by a sample of H atom:
Δ n ( Δ n + 1 ) 2 \frac{\Delta n(\Delta n+1)}{2} 2 Δ n ( Δ n + 1 )
9. Heisenberg’s uncertainty principle:
Δ x . Δ p > h 4 π o r m Δ x ⋅ Δ v ≥ h 4 π o r Δ x . Δ v ≥ h 4 π m \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} Δ x . Δ p > 4 π h o r m Δ x ⋅ Δ v ≥ 4 π h o r Δ x . Δ v ≥ 4 π m h 10. Quantum Numbers:
Principal quantum number ( n ) = 1 , 2 , 3 , 4 … . . t o ∞ (n)=1,2,3,4 \ldots . . to\: \infty ( n ) = 1 , 2 , 3 , 4 … . . t o ∞ Orbital angular momentum of electron in any orbit = n h 2 π =\frac{ nh }{2 \pi} = 2 π n h 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 = h 2 π ℓ ( ℓ + 1 ) = ℏ ℓ ( ℓ + 1 ) [ ℏ = h 2 π ] \frac{ h }{2 \pi} \sqrt{\ell(\ell+1)}=\hbar \sqrt{\ell(\ell+1)}\left[\hbar=\frac{h}{2 \pi}\right] 2 π h ℓ ( ℓ + 1 ) = ℏ ℓ ( ℓ + 1 ) [ ℏ = 2 π h ]
