# Question #d7a4c

Nov 13, 2016

Photo+electric effect = The effect caused by emission of electron due to photons

#### Explanation:

The word photoelectric effect means emission of electrons due to photons.

It is given by Albert Einstein. When light photons with suitable energy shone on a metal it emits electrons.

The maximum kinetic energy of ejected electron is

${K}_{\max} = h \nu - W$

Where,

$h$ = Planck's constant

$\nu$ = frequency of incident photons

$W$ = Work function of material

Since work function is the minimum energy required to remove delocalised electron from surface of metal it's value is

$W = h {\nu}_{\circ}$

Where ${\nu}_{\circ}$ = threshold frequency for the metal

Then kinetic energy now becomes

${K}_{\max} = h \left(\nu - {\nu}_{\circ}\right)$

Kinetic energy is positive so we must have $\nu > {\nu}_{\circ}$ for the photoelectric effect to occur.

2nd part of the question is How is it significant to the development of atomic model

With the help of photoelectric effect it is clear that electrons and photons behaves like a particle. (Like how 2 balls collide and goes apart)

Performing other experiments Einstein has suggested light can behave like a particle as well as wave i.e it has dual character.

de-Broglie suggested that just as light exhibit wave and particle properties, all microscopic material particles such as electrons, photons, atoms, molecules etc. have also dual character.

Thus according to de-Broglie all material particles in motion possess wave characteristics. and the wavelength associated with a particle of mass $m$ moving with a velocity $v$ is given by the relation

$l a m \mathrm{da} = \frac{h}{m v} = \frac{h}{p}$

Since electron moves as a wave we can assume the following diagram Her we can write circumference = $n l a m \mathrm{da}$

$2 \pi r = n l a m \mathrm{da}$ (Take $r$ as radius)

But according to de-Broglie $l a m \mathrm{da} = \frac{h}{m v}$

$\therefore 2 \pi r = \frac{n h}{m v}$

or $m v r = \frac{n h}{2 \pi}$

Thus angular momentum of electron should be an integral multiple of h/2$\pi$. In other words, the angular momentum is quantised. This the same as Bohr's condition for quantisation of angular momentum of fixed energy orbits

Hence de-Broglie equation helped in explaining Bohr's postulate regarding the quantisation of an electron.