Question

According to Heisenberg's uncertainty principle, the product of uncertainties in position and velocities for an electron of mass 9.1 $\times$ ${10}^{-31}$ kg is

• A. 2.8 $\times$ ${10}^{-3}$ $m^2$ $s^{-1}$
• B. 3.8 $\times$ ${10}^{-5}$ $m^2$ $s^{-1}$
• C. 5.8 $\times$ ${10}^{-5}$ $m^2$ $s^{-1}$
• D. 6.8 $\times$ ${10}^{-6}$ $m^2$ $s^{-1}$

Answer 1

The correct option is C

5.8 $\times$ ${10}^{-5}$ $m^2$ $s^{-1}$

We know ,from Heisenberg Uncertainty Principle,

$△x$ $\times$ $△p$ = $\frac{h}{4\pi }$

$\Rightarrow$ $△x$ $\times$ $△v$ = $\frac{h}{4\pi m}$

Given that mass of electron = 9.1 $\times$ ${10}^{-31}$ kg

Plank's constant = 6.63 $\times$ ${10}^{-34}$ kg $m^2$ $s^{-1}$

By using $△x$ $\times$ $△v$ = $\frac{h}{4\pi \times m}$ ;

Where: $△$ x = uncertainty in position

$△$ v = uncertainty in velocity

$△x$ $\times$ $△v$ = $\frac{h}{4\pi m}$
= $\frac{6.63\times {10}^{-34}}{4\times 3.14\times 9.1\times {10}^{-31}}$ = 5.8 $\times$ ${10}^{-5}$ $m^2$ $s^{-1}$