﻿ Formulas realted to Structure of atom || chemistry

# Structure of atom

Atomic number
Atomic number (Z) = Number of protons in the nucleus of an atom or
Number of electrons in a neutral atom

Mass number
Mass number (A) = Number of protons + number of neutrons

Number of neutrons
Number of neutrons = Mass number (A) - Atomic number (Z)

Speed of light
Speed of light = product of frequency and wavelength of light
c = vλ

According to Planck's quantum theory
E= hv

Einstein's photoelectric equation
$$hv = hv_{\,o} + \frac {1}{2}m_{\,o}v^{2}$$

Line spectrum of hydrogen
$$\overline{v} = 109677(\frac {1}{n_{1}^{2}} -\frac {1}{n_{2}^{2}})cm^{-1}$$ $$\text{where }\overline{v} \text{ is wave number and } \overline{v} = \frac {1}{\lambda}$$ n1 = 1, 2, 3, ....
n2 = n1 + 1, n1 + 2,....

Total number of nodes
Total number of nodes = n-1
Radial nodes = n - l -1
Angular nodes = l

Number of subshells
Number of subshells in nth = n
Number of orbitals in nth = n2
Number of electrons in nth =2n2
Number of orbitals in subshell = 2l + 1
Number of electrons in subshell = 2(2l + 1)

Bohr's model of hydrogen atom
1. Frequency of radiation absorbed or emitted during transition $$v = \frac {\Delta E}{h}$$ $$v = \frac{E_{\,2} - E_{\,1}}{h}$$ where E1 = Energy of lower energy state
where E2 = Energy of higher energy state
2. Orbit angular momentum of an electron
$$m_{\,o}vr =n\cdot \frac {h }{2 \pi}$$ where n = 1, 2, 3 ....
3. Energy of stationary states
$$E_{\,n} = -2.18 \times 10^{15}( \frac {Z^{2} }{n^{2} })J$$ 4. Radii of stationary states/orbits
$$r_{\,n} = 52.9 \times (\frac {n^{2} }{Z })pm$$