Question

Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of a proton moving at a speed of ( 5.10 ±0.01)×104m/s. ( Take the mass of a proton m=1.673×10−27kg.)

Answer 1

Answer: The uncertainty in proton's position is $6.307\times 10^{-10}m$

Explanation:

The equation representing Heisenberg's uncertainty principle follows:

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

where,

$\Delta x$ = uncertainty in position = ?

$\Delta p$ = uncertainty in momentum  = $m\Delta v$

m = mass of the particle = $1.673\times 10^{-27}kg$

$\Delta v$ = uncertainty in speed = $0.01\times 10^{4}m/s$

h = Planck's constant = $6.627\times 10^{-34}kgm^2/s^2$

Putting values in above equation, we get:

$\Delta x.(1.673\times 10^{-27}\times 0.01\times 10^4)=\frac{6.627\times 10^{-34}kgm^2/s^2}{2\times 3.14}\\\\\Delta x=\frac{6.627\times 10^{-34}}{2\times 3.14\times 1.673\times 10^{-27}\times 0.01\times 10^4}=6.307\times 10^{-10}m$

Hence, the uncertainty in proton's position is $6.307\times 10^{-10}m$