Uncertainty in the position of an electron (mass = 9.1 × 10^–31 kg) moving with a velocity 300 ms–1, accurate upto 0.001%, will be

19.2 × 10^–2 m

5.76 × 10^–2 m

1.92 × 10^–2 m

3.84 × 10^–2 m

Solution

1.92 × 10^–2 m

increment straight x. increment straight v space greater or equal than space fraction numerator straight h over denominator 4 πm end fraction increment straight x space greater or equal than space fraction numerator straight h over denominator 4 πm increment straight V end fraction space equals space fraction numerator 6.63 space straight x space 10 to the power of negative 34 end exponent over denominator 4 space straight x space 3.14 space straight x space 9.1 space straight x space 10 to the power of negative 31 end exponent space straight x space 300 space straight x space begin display style fraction numerator 0.001 over denominator 100 end fraction end style end fraction space equals space fraction numerator 6.63 space straight x space 10 to the power of negative 34 end exponent over denominator 4 space straight x space 3.14 space straight x space 9.1 space straight x space 3 space straight x space 10 to the power of negative 31 end exponent space straight x space 10 to the power of negative 3 end exponent end fraction space equals space 0.01933 space equals space 1.93 space straight x space 10 to the power of negative 2 end exponent

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