German physicist Werner Heisenberg related the uncertainty of an object\\\'s pos

Question

German physicist Werner Heisenberg related the uncertainty of an object's position (?x) to the uncertainty in its velocity ?v.

German physicist Werner Heisenberg related the uncertainty of an object's position (Ax) to the uncertainty in its velocity Ax 2 where h is Planck's constant and m is the mass of the object. The mass of an electron is 9.11x 10-3 kg. What is the uncertainty in the position of an electron moving at 3.00 x 106 m/s with an uncertainty of Av = 0.01 106 m/s? Number 117,274× 10-8 Im IIn

Explanation / Answer

Given that uncertainity in velocity = 0.01 x 106 m/s

   mass of elecron = 9.11 x 10-31 kg

Heisenberg uncertainity priciple is

x . mv = h/4

x = uncertainity in position

v = uncertainity in velocity = 0.01 x 106 m/s

m = mass of elecron = 9.11 x 10-31 kg

h = planck's constant = 6.626 x 10-34 J.s

Therefore,

  x . mv = h/4

  x = (h/4) (1/mv)

= [(6.626 x 10-34 J.s/ 4)] [1/ (9.11 x 10-31 kg) (0.01 x 106 m/s)]

= 5.8 x 10-9 m

  x = 5.8 x 10-9 m

Therefore,

uncertainity in the position of electron = 5.8 x 10-9 m

  

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