The photoelectric effect  :  

E = energy of a photon =   and  E = m c²

 . . (1)      Einstein photoelectric equation

                     where = work function of the metal = h f_o

The reverse potential difference V is increased to the point ( called stopping potential V_S ) at which the current is just stopped altogether.

The maximum kinetic energy of the electrons is

= e V_S.........(2)

Combine (1) and (2) gives,     

The hydrogen spectrum

In 1913. Bohr postulated that :

(1) electrons in atoms occupy certain discrete orbits defined by m v r = n h/ (2 p),

(2) when an electron jumps from one stable orbit to another orbit of lower energy, a quantum of radiation is emitted.           h f = E₂ - E₁ 

           where 1 eV = 1.6 X 10^-19 J  and

                                               Ionization energy = 13.6 eV

de Broglie wavelength :           for photon

                                              for electron wave

X-rays

The efficiency of the tube depends on target element. The high the atomic number of a target material, the higher the efficiency

The penetrating power of the X-rays depends on the p.d. across the X-rays tube.

The intensity of the beam depends on the number of electrons striking the target per second.

The continuous spectrum of X-rays

minimum wavelength λ_min is given by

In general,  

The line spectrum of X-rays

X-ray spectra are due to energy changes in electrons close to the nucleus of metals.