Question

If uncertainty in the measurement of position and momentum of an electron are equal, then uncertainty in the measurement of its velocity is approximately is 8 $\times$ 10${}^x$ m s${}^{-1}$
value of x is............

Answer 1

$\Delta$x.$\Delta$p $\ge h/4\pi$

$\Rightarrow$ $\Delta$p $\ge$ $\sqrt{\frac{h}{4\pi }}$ [$\because$ $\Delta$x = $\Delta$p(given)]

$\Rightarrow$ m$\ast$ $\Delta$V $\ge$ $\sqrt{\frac{h}{4\pi }}$ [$\because$ $\Delta$p = m$\Delta$v]

$\Rightarrow$ $\Delta$V $\ge$ $\frac{1}{m}$ $\sqrt{\frac{h}{4\pi }}$ $=$ 8 $\times$ 10${}^{12}$ ms${}^{-1}$