The French physicist Louis de Broglie in 1924 postulated that matter , like radiation , should exhibit dual behaviour. He proposed the following relationship between the wavelenght lambda of a material particle , its linear momentum p and planck cosntant h.
`lambda= (h)/(p)=(h)/(mv)`
The de Broglie relation implies that the wavelength of a partices should decreases as its velocity increases. It also implies that the for a given velocity heavir particule should have shorter wavelenght than lighter particles. The waves associated with particles in motin are called matter waves or de Broglie waves.
These waves differ from the electromagnetic waves as they
(i) have lower velocities
have no electrical and magnetic fields and
are not emitted by the particle under consideration.
The experimental confirmation of the de Broglie relation was obtained when Davisson and Germer. in
1927, observed that a beam of electrons is diffracted by a nickel arystal. As diffarceted by a nickel . As diffraction is a characteristic
property of waves, hence the beam of electron dehaves as a wave, as proposed by de Broglie.
Werner Heisenberg cobnsiderd the imits of how precisely we can measure propoerties of an electron or
other microscopic particle like electron. he determined that there is accurately we measure the momentum of a
particle, the less accurately we can determine its position . The converse is laso true . The is summed up
in what we now call the "Hesienberg uncertainty princple: It isimpossibble to determine simultameously ltbr. and percisely both the momentum ans position of particle . The product of uncertainly in the position,
Deltax and the ncertainly in the momentum Delta(mv) mudt be greater than or equal to `(h)/(4pi)` i.e.
`etaDeltax Delta(mv)ge(h)/(4pi)`
The correct order of wavelenght of Hydrogen `(._(1)H^(1))` Deuterium `(._(1)H^(2))` and Tritium `(._(1)H^(3))` moving withsame kinetic energy is.

Options

A. `lambda_(H)gtlambda_(D)gtlambda_(T)`
B. `lambda_(H)=lambda_(D)=lambda_(T)`
C. `lambda_(H)ltlambda_(D)ltlambda_(T)`
D. `lambda_(H)ltlambda_(D)gtlambda_(T)`

Answer

A

Explanation

`lambda=(h)/sqrt(2m.KE)`
for same KE `lambdapropto(1)/sqrt(m)`
so`lambda_(H)gtlambda_(0)gtlambda_(T)`