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Q.

The minimum uncertainty in the speed of an electron in an one dimensional region of length2a0 (Where  a0=Bohr  radius  52.9  pm) is ___________ km  s1

(Given mass of electron =9.1×1031  kg,  Planck's  constant  h=6.63×1034  Js

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answer is 548.

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Detailed Solution

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Heisenberg’ uncertainty principle

Δx×Δpxh4π

2a0×mΔvx=h4π(minimum)

Δvx=h4π×12a0×1m

=6.63×10344×3.14×2×52.9×1012×9.1×1031

=548273  ms1

=548.273  kms1

=548  km  s1

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The minimum uncertainty in the speed of an electron in an one dimensional region of length2a0 (Where  a0=Bohr  radius  52.9  pm) is ___________ km  s−1(Given mass of electron =9.1×10−31  kg,  Planck's  constant  h=6.63×10−34  Js