de-Broglie proposed dual natrue for elecrton by putting his famous equation ` lambda = ( lambda) /( mu)`, Later on Heisenberg proposed uncertiainty principle as . `Deltap.Deltaxle(h)/(2)(h=(h)/(2pi))` . On the contray particel natrue of electron wa estabilshed on the basis fo photoelectric effect . When a photon strikes the metal suface it given up its energy to the electro . Part of this enrgy ( say W) is used by the electrons to escpe form the metal and the remaining imparts he kinetc enrgy `(1//2 mu^2)` to photoeleton . The potential applied on the surface to reduce the velocity fo photoelecton to zero is known as stoppong potential .
If uncettainties in position and momentum of an electron are same them unceratinty in its velocity can be given by :

Options

A. ` ge sqrt ( h/( 4 pi m^2)`
B. `sqrt ( u lambda)/( 4 pi m)`
C. `ge sqrt (h)/( 2 m^2)`
D. Either of these

Answer

D

Explanation

`Delta u = Delta p `
` :. (Delta p)^2 ge h/( 2 4 pi)` ltbRgt ` (Delta um)^2 ge h/( 4pi)`
` :. Delta u ge sqrt (h/(4 pim^2) ge sqrt (( 4 lambda)/( 4 pi m)) ge sqrt (h/(2m^2))`
` ( h = h/ (2pi) and lambda= h/(mu))`.