Question

Question #d68af

Answer 1

`approx1.980xx10^-11m`

Explanation:

Heisenberg's uncertainty principle or simply called Uncertainty Principle states that for any particle it is impossible to know simultaneously both position and momentum precisely.
Mathematically stated

`Deltax*Delta p approxh` .......(1)

where `Deltax` is uncertainty in position, `Delta p` is uncertainty in momentum, and `h` is Planck's Constant and is `6.626xx 10^(-34) m^2 kg // s`.

Given in the problem uncertainty in speed of a proton `=+-0.01xx10^4ms^-1`
`=> Delta v=0.02xx10^4ms^-1`
`:.` uncertainty in momentum `Delta p=m_pxxDeltav`
`=1.673 xx 10^-27xx0.02xx10^4`
`=3.346xx10^-25`
Inserting in (1) the known and calulated values
`Deltax approx(6.626xx 10^(-34))/(3.346xx10^-25)`
`approx1.980xx10^-11m`

It is worth noting here that this value is larger than the diameter of the hydrogen nucleus. Which is size of proton itself and is in the range of `1.75 fm (1.75xx10^(−15) m)`.