In an atom, an electron is moving with a speed of 600 m / s with an accuracy of 0 . 005 % . Certainty with which the position of the electron can be located is ( h = 6 . 6 × 10 - 34 kg m 2 s - 1 , mass of electron, m e = 9 . 1 × 10 - 31 kg )

Step-by-step solution

Given that velocity of electron, v = 600   m / s Accuracy of velocity = 0.005 % According to Heisenberg's uncertainty principle Δx . mΔv = h 4 π ∆ v = 0 . 005 % or 600   m   s - 1 = 600 × 0 . 005 100 = 0 . 03 ∆ x × 9 . 1 × 10 - 31 × 0 . 03 = 6 . 6 × 10 - 34 4 × 3 . 14 Hence, ∆ x = 6 . 6 × 10 - 34 4 × 3 . 14 × 0 . 03 × 9 . 1 × 10 - 31 = 1 . 92 × 10 - 3   m