Question

If the uncertainty in the position of an electron is zero, then the uncertainty in it's momentum would be _____.

• A. zero
• B. $\ge$h/4$\pi$
• C. $\le$h/4$\pi$
• D. infinite

Answer 1

The correct option is D infinite

Heisenberg's uncertainty principle states that it is impossible to determine both the position and the momentum of an electron inside an atom simultaneously.

Mathematically, it is derived that the product of uncertainties in position and momentum is greater than or equal to a constant $\frac{\text{h}}{4\pi }$. The equation for that is:

$\Delta \text{x}.\Delta \text{p}\ge \frac{\text{h}}{4\pi }$ where,

$\Delta \text{x}$ = Uncertainty in position
$\Delta \text{p}$ = Uncertainty in momentum
$\text{h}$ = Planck's constant

$\Delta \text{p}\ge \frac{\text{h}}{4\pi \Delta \text{x}}$

If the uncertainty in position, $\Delta \text{x}$ = 0 then,
$\Delta \text{p}\ge \frac{\text{h}}{4\pi \text{.0}}$
$\Delta \text{p}$ = $\infty$
(since, dividing any finite number by zero gives infinity)

therefore, uncertainty in momentum, $\Delta \text{p}$ = $\infty$.