A ball weighing 10 g is moving with a velocity of $90 m s^{- 1} .$ If the uncertainty in its velocity is 5%, then the uncertainty in its position is ……… $\times 10^{- 33} m$ (Rounded off to the nearest integer) [Given, $h = 6.63 \times 10^{- 34} J - s$ ]

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Detailed Solution

According to Heisenberg’s uncertainty equation, $Δ \times \times m Δ v \geq \frac{h}{4 π}$

$(∴ m = 10 g = 10 \times 10^{- 3} k g, v = 90 m s^{- 1})$ uncertainty in position, $Δ x = \frac{h}{4 π} \times \frac{1}{(10 \times 10^{- 3}) \times (90 \times \frac{5}{100})} m$

$= 1.17 \times 10^{- 33} m ≃ 1 \times 10^{- 33} m$

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