QJEEM21Chfe0c: JEE Main 2021 Chemistry - Class 11 JEEM21Chfe0c Solution: An accelerated electron has a speed of 5 × 10 6 ms − 1 with an…

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An accelerated electron has a speed of 5

\times

10⁶ ms^{$-$ 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} kg, h =6.63

\times

10^{$-$ 34} Js,

π

= 3.14]

Accepted Answer

Δ v = \frac{0.02}{100} \times 5 \times 10^{6} = 10^{3}

m/s

Δ x . Δ v = \frac{h}{4 π m}

\Rightarrow

x \times 10^{- 9} \times 10^{3} = \frac{6.63 \times 10^{- 34}}{4 \times 3.14 \times 9.1 \times 10^{- 31}}

\Rightarrow

x \times 10^{- 9} \times 10^{3} = 0.058 \times 10^{- 3}

\Rightarrow

x = \frac{0.058 \times 10^{- 6}}{10^{- 9}} = 58

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