If the uncertainty in the position of a moving electron is equal to its de Broglie wavelength, then its velocity will be completely uncertain. Explain.

Explanation

By de-Broglie equation :
`lambda = h/P`
But, `lambda = Delta x` (given)
`:. Delta x = h/p`
According to Heisenberg uncertainty principle,
`Delta x cdot Delta p ge h/(4 pi)`
`h/p Delta p ge h/(4pi)`
or `h/(mv) cdot m Delta v h/(4pi)`
or `(Delta v)/v ge 1/(4pi)`
or `Delta v ge v/(4 pi)`
Thus, uncertainty in velocity is so large that its velocity in uncertain.