Answer:
The kinetic energy of an electron is [tex]1.54\times10^{-15}\ J[/tex]
Explanation:
Given that,
Distance = 0.1 nm
We need to calculate the momentum
Using uncertainty principle
[tex]\Delta x\Delta p\geq\dfrac{h}{4\pi}[/tex]
[tex]\Delta p\geq\dfrac{h}{\Delta x\times 4\pi}[/tex]
Where, [tex]\Delta p[/tex] = change in momentum
[tex]\Delta x[/tex] = change in position
Put the value into the formula
[tex]\Delta p=\dfrac{6.6\times10^{-34}}{4\pi\times10^{-10}}[/tex]
[tex]\Delta p=5.3\times10^{-23}[/tex]
We need to calculate the kinetic energy for an electron
[tex]K.E=\dfrac{p^2}{2m}[/tex]
Where, P = momentum
m = mass of electron
Put the value into the formula
[tex]K.E=\dfrac{(5.3\times10^{-23})^2}{2\times9.1\times10^{-31}}[/tex]
[tex]K.E=1.54\times10^{-15}\ J[/tex]
Hence, The kinetic energy of an electron is [tex]1.54\times10^{-15}\ J[/tex]
