Question

Calculate the uncertainty in the position of an electron, if the uncertainty in its velocity is 0.01% in first Bohr's orbit of hydrogen.

• A. 265.9 nm
• B. 2.65 nm
• C. 26.5 nm
• D. 265 $\stackrel{\circ }{A}$

Answer 1

The correct option is A 265.9 nm

Given:
Mass of electron = $9.1\times {10}^{-31}$ Kg
Velocity of the electron in the first Bohr's orbit of hydrogen atom = $2.18\times {10}^6$ m/sec
$\Delta v=\frac{0.01}{100}\times 2.18\times {10}^6=2.18\times {10}^2$ m/sec
$\Delta x\Delta p\ge \frac{h}{4\pi }$
$\Delta x\ge \frac{h}{4\pi m\Delta v}$
$\Delta x\ge \frac{6.626\times {10}^{-34}}{4\times 3.14\times 9.1\times {10}^{-31}\times 218}$
$\Delta x\ge$ 265.9 nm