Question

uncertainty in angular position of electron in bohr orbit is ​

Answer 1

The uncertainty relation between linear momentum and position of electron in Bohr's orbit is given by,

$\boxed{\bf{\Delta P.\Delta x\geq\frac{h}{4\pi}}}$.......(1)

Consider an electron with linear momentum p moving on a circle of radius r. The electronʹs angular

momentum is given by

$L=mvr=P.r$......(2)

in moving a distance x on the circle, the electron sweeps out an angle $\theta$ in radians.

so, $\theta=\frac{x}{r}$......(3)

equations (2) and (3) suggest,

$\Delta P=\frac{\Delta L}{r}$ and $\Delta x=\Delta\theta.r$

now, put these expressions in equation (1),

so, $\boxed{\bf{\Delta L.\Delta\theta\geq\frac{h}{4\pi}}}$ is required expression.