A dust particle has mass equal to 10-11g, diameter 10-4cm and velocity 10-4cm/s. The error in measurement of velocity is 0.1%. What will be the uncertainty in its position?

Question

A dust particle has mass equal to 10-11g, diameter 10-4cm and velocity 10-4cm/s. The error in measurement of velocity is 0.1%. What will be the uncertainty in its position? (A)  ~0.527× 1010 text cm  (B)  ~5.27× 109 text cm  (C)  0.527× 10-15cm  (D)  0.527× 10-9cm

Tardigrade Admin · Accepted Answer

v=10-4cm s-1 ∴ Δ v=(0.1× 10-4/100) (due to 1% error) =1× 10-7cm s-1 Now, Δ v.Δ x=(h/4π m) ∴ Δ x=(6.626× 10-27/4× 3.14× 10-11× 10-7) =0.527× 10-9cm

Q. A dust particle has mass equal to $10^{- 11} g,$ diameter $10^{- 4} c m$ and velocity $10^{- 4} c m / s .$ The error in measurement of velocity is $0.1$ What will be the uncertainty in its position?

$0.527 \times 10^{10} c m$

$5.27 \times 10^{9} c m$

$0.527 \times 10^{- 15} c m$

$0.527 \times 10^{- 9} c m$

$v = 10^{- 4} c m s^{- 1}$
$∴$ $Δ v = \frac{0.1 \times 10 ^{- 4}}{100}$
(due to 1% error)
$= 1 \times 10^{- 7} c m s^{- 1}$
Now, $Δ v .Δ x = \frac{h}{4 πm}$
$∴$ $Δ x = \frac{6.626 \times 10 ^{- 27}}{4 \times 3.14 \times 10 ^{- 11} \times 10 ^{- 7}}$
$= 0.527 \times 10^{- 9} c m$

Q. A dust particle has mass equal to 10−11g, diameter 10−4cm and velocity 10−4cm/s. The error in measurement of velocity is 0.1 What will be the uncertainty in its position?

0.527×1010cm

5.27×109cm

0.527×10−15cm

0.527×10−9cm