Question

If an electron is moving with the velocity of 600 ms^-1 which is accurate upto 0.005% & Calculate the uncertainty in its position.

Answer 1

del.v=600 ms-1
=600×5/1000
=3ms-1
del.x=h/4×3.14×3
=6.626×10-34/12.56×3
=0.175×10-35

Answer 2

Answer : The uncertainty in its position is, $1.92\times 10^{-3}m$

Explanation : Given,

Velocity of electron = $600m/s$

Accuracy of velocity of electron = 0.005%

First we have to calculate the accurate velocity of electron.

$\Delta v=600m/s\times \frac{0.005}{100}=0.03m/s$

Now we have to calculate the uncertainty in its position.

Formula used :

$\Delta x\times \Delta p=\frac{h}{4\pi}$

$p=m\times v$

$\Delta x\times m\times \Delta v=\frac{h}{4\pi}$

where,

$\Delta x$ = ?

$\Delta v$ = 0.03 m/s

m = mass of electron = $9.1\times 10^{-31}kg$

h = Planck's constant = $6.6\times 10^{-34}Js$

Now put all the given values in the above formula, we get:

$\Delta x\times (9.1\times 10^{-31}kg)\times (0.03m/s)=\frac{6.6\times 10^{-34}Js}{4\times 3.14}$

$\Delta x=1.92\times 10^{-3}m$

Therefore, the uncertainty in its position is, $1.92\times 10^{-3}m$