Question

If the uncertainty in the position of an electron is zero, the uncertainty in its momentum will be .

• A. zero
• B. infinite
• C. $\frac{h}{2\pi }$

Answer 1

The correct option is B infinite

According to Heisenberg's uncertainty principle, both position and momentum of an electron cannot be determined simultaneously.

Mathematically,

$\Delta p\times \Delta x\ge \frac{h}{4\pi }$
Since the uncertainty in the position of the electron is zero, $\Delta x$ = 0

Hence, for an electron
$\Rightarrow \Delta p\times 0\ge$ $\frac{h}{4\pi }$
$\Rightarrow \Delta p$ = $\frac{h}{4\pi \times 0}=\infty$
[Since anything divided by zero is infinite]

Therefore, the uncertainty in its momentum, ($\Delta p$) should be indeterminate (infinite).