Question

If uncertainty in the measurement of position and momentum of an electron are equal then uncertainly in the measurement of its velocity is approximately:

• A. 8 x 10¹² ms^-1
• B. 4 x 10¹² ms^-1
• C. 6 x 10¹² ms^-1
• D. 2 x 10¹² ms^-1

Answer 1

The correct option is A

8 x 10¹² ms^-1

Do you know about Heisenberg Uncertainty Principle?

Heisenberg's uncertainty principle is

$△x$ $△p$ $\ge$ $\frac{h}{4\pi }$ Given $△x$ = $△p$ = m$△$v

$\Rightarrow$ $△p$ $\ge$ $\sqrt{\frac{h}{4\pi }}$ i.e m$△v$ $\ge$ $\sqrt{\frac{h}{4\pi }}$

$\Rightarrow$ $△v$ $\ge$ $\frac{1}{m}$ $\sqrt{\frac{h}{4\pi }}$ $\ge$ 8 $\times$ ${10}^{12}$ m $s^{-1}$