Question

An electron exists within a region of 10^ -10 m, find its momentum uncertainty and approximate K.E..??

Answer 1

An electron exists within a region of $10^{\wedge} - 10\mathrm{m}$, find its momentum uncertainty and approximate K.E..??

Uncertainty principle:

$$\Delta p \Delta x \geq \frac {h}{2 \pi}$$

$\Delta p$ and $\Delta x$ - momentum uncertainty and position uncertainty

$h$ - Planck constant

Therefore:

$$\Delta p \approx \frac {h}{2 \pi \Delta x} = 6.63 \frac {10^{-34} J s}{2 \pi 10^{-10} m} = 1,110^{-24} k g \frac {m}{s}$$

approximate K.E. equals:

$$T = \frac {\Delta p ^ {2}}{2 m _ {e}} = \frac {\left(1 , 1 1 0 ^ {- 2 4} k g \frac {m}{s}\right) ^ {2}}{2 * 9 . 1 1 0 ^ {- 3 1} k g} = 6.1 1 0 ^ {- 1 9} J$$

$m_{e}$ - electron mass

Answer: momentum uncertainty $= 1,110^{-24}kg\frac{m}{s}$, kinetic energy $= 6.110^{-19}J$