Question

Show that if the measurement of the uncertainty in the location of the particle is equal to its de Broglie wavelength, the minimum uncertainty in its velocity is equal to its velocity / 4

Answer 1

From the uncertainty principle ⇒ Uncertainty is known as the measurement of momentum.

Δx . Δp = h
Here Δx = λ = h/p

Now , from the principle.
Δx . Δp = h/4π . -----→(a)

Δx . mΔv = h/4π  { p =mv}

h/p . (mΔv) = h/4π 
$\frac{h}{mv}$  mΔv = h/4π

Now substitute this value in eq (a).

h/mv × (mΔv) ≥ 4π .
Hence
Δv ≥ v/4π .

Hence proved.

Hope it Helps. :-)