Question

Question #5e7e8

Answer 1

`Δv>=2.895*10^5` (m/s)

Explanation:

Werner Karl Heisenberg found the uncertaintry principle in 1927.
The formula is `color(red)(ΔxΔp>=ħ/2)`, where
`Δx`: uncertainty of place
`Δp`: uncertainty of momentum
`ħ`: Dirac's constant (`ħ=h/(2pi)=1.055*10^-34" "(J*s)`

Let `m` the mass of electron and `Δv` the uncertainty of speed.
(`m=9.109*10^-31 kg`).

`Δp=mΔv`
`mΔxΔv>=ħ/2`
`Δv>=ħ/(2mΔx)`
`=(1.055*10^-34" "(J*s))/(2*9.109*10^-31 (kg) * 2.00*10^-10 (m))`
`=2.895*10^5` (m/s).

This may seem so large. However, it is only about one-thousandth of the speed of light(`c=2.99*10^8` m/s).