Cheat Sheet (Pinned): Quick Reference for NEET Day

type: cheat_sheet | pinned: true | subtopic: Final Revision

BOHR MODEL

Formula	Value/Expression
r_n	0.529 × $n^{2}$ /Z Å
v_n	$2.18 \times 10^{6}$ × Z/n m/s
E_n	−13.6 $Z^{2}$ / $n^{2}$ eV
KE_n	+13.6 $Z^{2}$ / $n^{2}$ eV (= −E_n)
PE_n	−27.2 $Z^{2}$ / $n^{2}$ eV (= 2E_n)
L_n	nℏ = nh/(2π)
Ground state H	r_{1}=0.529Å, v_{1}= $2.18 \times 10^{6}$ m/s, $E_{1}$ =−13.6eV

SPECTRAL SERIES

Series	n_{1}	Region	First Line	Series Limit
Lyman	1	UV	121.6 nm	91.2 nm
Balmer	2	Visible	656.3 nm (red)	364.6 nm
Paschen	3	IR	1875 nm	820.4 nm

$\frac{1}{\lambda} = RZ^2\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right), \quad R = 1.097 \times 10^7\ \text{m}^{-1}$

Spectral lines from level n: N = n(n−1)/2

NUCLEAR PHYSICS

$R = 1.2 \times $A^{1/3}$\ \text{fm} \qquad \rho_{\text{nucleus}} \approx 2.3 \times 10^{17}\ \text{kg/m}^3\ (\text{constant})$ $\Delta m = [Zm_p + (A-Z)m_n] - M \qquad BE = \Delta m \times 931.5\ \text{MeV}$ Fe-56: most stable (BE/A ≈ 8.75 MeV/n). Fusion (light) and Fission (heavy) both release energy.

RADIOACTIVE DECAY

$N = N_0 $e^{-\lambda t}$ = \frac{N_0}{2^n}\ (n \text{ half-lives}) \qquad t_{1/2} = \frac{0.693}{\lambda}$ $\tau = \frac{1}{\lambda} = 1.443\ t_{1/2} > t_{1/2} \qquad \text{Activity: } A = \lambda N$

DECAY TYPES

Type	$\Delta A$	$\Delta Z$	Emits
Alpha	−4	−2	He-4
β^{-}	0	+1	$e^{-}$ + ν̄
β^{+}	0	−1	$e^{+}$ + ν
γ	0	0	photon

KEY VALUES

a_{0} = 0.529 Å; $R_{0}$ = 1.2 fm; R = $1.097 \times 10^{7}$ $m^{-1}$ ; 1 u = 931.5 MeV/ $c^{2}$
k = $9 \times 10^{9}$ N· $m^{2}$ / $C^{2}$ ; e = $1.6 \times 10^{-1}$ ^{9} C; h = $6.626 \times 10^{-34}$ J·s; hc = 1240 eV·nm

DISTANCE OF CLOSEST APPROACH

$d = \frac{2kZe^2}{KE_\alpha} \quad [\text{upper limit on nuclear size}]$