### 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

** Energy of quantum of radiation **

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 **

$$ \overline{v} = 109677(\frac {1}{n_{1}^{2}} -\frac {1}{n_{2}^{2}})cm^{-1}$$
$$ \text{where }\overline{v} \text{ is wave number and } \overline{v} = \frac {1}{\lambda} $$
n_{1} = 1, 2, 3, ....

n_{2} = n_{1} + 1, n_{1} + 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 n^{th} = n

Number of orbitals in n^{th} = n^{2}

Number of electrons in n^{th} =2n^{2}

Number of orbitals in subshell = 2*l* + 1

Number of electrons in subshell = 2(2*l* + 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 E_{1} = Energy of lower energy state

where E_{2} = 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

$$ r_{\,n} = 52.9 \times (\frac {n^{2} }{Z })pm$$