Ncert Exercises & Solutions

Table-tennis ball has mass 10 g and speed of 90 m/s. If speed can be measured within an accuracy of 4%, what will be the uncertainty in speed and position?

Given that, speed=90 m/s

mass

$= 10 g = 10 \times 10^{- 3} kg$

Uncertainty in speed

$(∆ v) = 4 % of 90 {ms}^{- 1} = \frac{40 \times 90}{100} = 3.6 {ms}^{- 1}$

From Heisenberg uncertainty principle,

$∆ x \cdot ∆ v = \frac{h}{4 πm}$

$∆ x = \frac{h}{4 πm ∆ v}$

Uncertainty in position,

$∆ x = \frac{6.626 \times 10^{- 34} kg m^{2} s^{- 1}}{4 \times 3.14 \times 10 \times 10^{- 3} kg \times 3.6 {ms}^{- 1}}$

$= 1.46 \times 10^{- 33} m$

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