Question

The uncertainty in the position of an object weighing 40 g is $\pm {10}^{-3}m$. Calculate the uncertainty in its velocity.

• A. $1.32\times {10}^{-30}m/s$
• B. $2.63\times {10}^{-29}m/s$
• C. $0.55\times {10}^{-30}m/s$
• D. $4.55\times {10}^{-29}m/s$

Answer 1

The correct option is A $1.32\times {10}^{-30}m/s$

From Heisenberg’s uncertainty principle,
Δx. (Δp) ≥ $\frac{h}{4\pi }$
$\Rightarrow \Delta x.m.\left(\Delta v\right)\ge \frac{h}{4\pi }$
Where, h = Planck’s constant
Δx = uncertainty in position = ${10}^{-3}m$
Δv = uncertainty in velocity
m = mass of the bullet in kilograms = $40\times {10}^{-3}kg$
So, $\Delta v\ge \frac{h}{4\pi \Delta xm}....\left(1\right)$

Putting up the values in eq. (1)
$\Delta v\ge \frac{6.6\times {10}^{-34}}{4\times 3.14\times {10}^{-3}\times 40\times {10}^{-3}}\Delta v\ge 1.313\times {10}^{-30}m/s$