Question

uncertainty in momentum is twice the uncertainty in position then uncertainty in velocity will be what?

Answer 1

The answer is in the image hope u r satisfied

Answer 2

Answer: The uncertainty in velocity is equal to $\frac{1}{m}\time \sqrt{\frac{h}{2\pi}}$

Explanation:

Heisenberg's uncertainty principle is  given by the equation:

$\Delta x.\Delta p=\frac{h}{4\pi}$

We are given:

Uncertainty in momentum is twice the uncertainty in position, this means that:

$\Delta p=2\Delta x$

And,

$\Delta p=m\Delta v$

Putting all the relations in above equation, we get:

$\Rightarrow \Delta x.m\Delta v=\frac{h}{4\pi}\\\\\Rightarrow \frac{\Delta p}{2}.\Delta v=\frac{h}{4\pi \times m}\\\\\Rightarrow m\Delta v.\Delta v=\frac{2h}{4\pi \times m}\\\\\Rightarrow (\Delta v)^2=\frac{h}{2\pi \times m^2}\\\\\Rightarrow \Delta v=\sqrt{\frac{h}{2\pi \times m^2}}\\\\\Rightarrow \Delta v=\frac{1}{m}\times \sqrt{\frac{h}{2\pi}}$

Hence, the uncertainty in velocity is equal to $\frac{1}{m}\time \sqrt{\frac{h}{2\pi}}$