What are the consequences that lead to the development of quantum mechanical model of an atom?

Explanation

In 1923 Louis de-Broglie proposed that like light matter also has dual character . It exhibits wave as well as particle nature . He derived an equation to calculate the wave-length `(lamda)` of the wave associated with a particle of mass m , nmoving with velocity v and it is given by
`lamda=(h)/("mv")" (or)"lamda=(h)/(p)`
'h' is Planck's constant and P is momentum of the particle . It may be noted that wave character has significance only in the case of sub-microscopic particles such as electrons.
The precise location of a wave cannot be predicted as a wave is not located at a particular point but extends in space . Thus the wave nature of electron puts some restriction in finding the position precisely . W . Heisenberg put forward this limitation in the form of uncertainty principle . According ot Heisenberg,
"It is not possible to determine simultaneously and accurately both the position and momentum of a small moving particle , such as electron."
It can be expressed mathematically as ,
`Delta"x"xxDeltapge(h)/(4pi)`
`Delta"x"xxmDeltavge(h)/(4pi)`
where `Deltax` = uncertainty in position
`Deltap` = uncertainty in momentum
m = mass of particle
`Deltav` = uncertainty in velocity
h = Planck's constant.
The uncertainty principle is due to the direct consequence of dual nature of matter .
A microscopic object such as electron has both observable wave - like and particle - like properties . The behaviour of such particles cannot be explained on the basis of science called quantum mechanical model of atom was developed . Quantum mechanics is a theroretical science that takes into account the dual nature of matter .