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Q.

An accelerated electron has speed of $5 \times 10^{6} m . s^{- 1}$ with an uncertainty of 0.02%. The uncertainty in finding its location while in motion is $x \times 10^{- 9} m$ . The value of x is ____ (nearest integer)
[use mass of electron $= 9.1 \times 10^{- 31} K g, h = 6.63 \times 10^{- 34} J s π = 3.14$ ]

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answer is 58.

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Detailed Solution

$Δ x . Δ p = \frac{h}{4 π} Δ x . m Δ v = \frac{h}{4 π} Δ v = 5 \times 10^{6} \times \frac{0.02}{100} Δ v = 10^{3} m / s Δ x = \frac{h}{4 π . m . Δ v} = \frac{6.63 \times 10^{- 34}}{4 \times 3.14 \times 9.1 \times 10^{- 31} \times 10^{3}} Δ x = 5.8 \times 10^{- 8} m = 58 \times 10^{- 9} m$

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An accelerated electron has speed of 5×106m.s−1 with an uncertainty of 0.02%. The uncertainty in finding its location while in motion is x×10−9m. The value of x is ____ (nearest integer)[use mass of electron =9.1×10−31Kg, h=6.63×10−34Js π=3.14]