Question

a) Explain Heisenberg's uncertainly principle with mathematical derivation.
b) Calculate the wavelength, frequency and wave number of light wave whose period is $2.0\times {10}^{-10}sec$

Answer 1

a) According to Heisenberg's uncertainty principle,

" it is not possible to determine simultaneously the position and momentum of a moving microscopic particle(electron) with absolute accuracy."

if $\Delta x$ is the uncertainty in the determination of the position and $\Delta p$ is the uncertainty in the determination of momentum of a very small moving particle then according to Heisenberg,

$\Delta x\Delta p=\frac{h}{4\pi }$

b) As $T=\frac{1}{f}$

$f=\frac{1}{2\times {10}^{-10}s}$

$f=5\times {10}^9{s}^{-1}$

Velocity of light is given by,

$v=f\lambda$

$\lambda =\frac{v}{f}$

$\lambda =\frac{3\times {10}^{8}m/s}{5\times {10}^9{s}^{-1}}$

$\lambda =6\times {10}^{-2}m$

Wave number=$\frac{1}{\lambda }$

Wave number=$16m^{-1}$