Question

Dual nature of matter was proposed by Louis de Broglie. 

(a) Calculate the de Broglie wavelength associated with an electron with velocity equal to that of light.

(b) State Heisenberg’s uncertainty principle and give its mathematical expression.

Answer 1

(a) Wave length, \(\lambda=\frac{h}{mv}\) 

= \(\frac{6.626\times10^{-34}Js}{9.11\times10^{-31}kg\times 3\times10^3ms^{-1}}\) = 2.424 x 10^-12m

(b) It states that it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron.

Mathematically, it can be given as in the equation

∆x ⇒ uncertainty in position of the particle 

∆px ⇒ uncertainty in momentum of the particle

∆vx ⇒ uncertainty in velocity of the particle

m ⇒ mass of the particle and 

h ⇒ the Planck’s constant