Atoms formulas

Bohr model

Quantised angular momentum

$\displaystyle mvr = \frac{nh}{2\pi}$

Radius of the nth orbit

$\displaystyle r_n = 0.529\,\frac{n^2}{Z}\ \text{Å}$

Speed in the nth orbit

$\displaystyle v_n = 2.19\times10^6\,\frac{Z}{n}\ \text{m/s}$

Energy of the nth orbit

$\displaystyle E_n = -13.6\,\frac{Z^2}{n^2}\ \text{eV}$

Energy of a photon

$\displaystyle h\nu = E_i - E_f$

Hydrogen spectrum

Rydberg formula

$\displaystyle \frac{1}{\lambda} = R\left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$

R ≈ 1.097 × 10⁷ m⁻¹.

Number of spectral lines

$\displaystyle N = \frac{n(n - 1)}{2}$

From level n down to level 1.

Series names

• Lyman ends at n = 1 (ultraviolet).
• Balmer ends at n = 2 (visible).
• Paschen ends at n = 3, Brackett at n = 4 and Pfund at n = 5 (all infrared).