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Q.

The uncertainty in the location of circulating electron is equal to its de Broglie wavelength. The minimum percent error in its measurement of velocity under this circumstances will be approximately

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a

4

b

8

c

18

d

22

answer is B.

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Detailed Solution

Let the electron be moving with momentum, p, its wavelength will be equal to h/p.λ=hp=∆xFrom Heisenberg's uncertainty principle,Δx × Δp  =  h4πΔpp=  14πMinimum percent error in measuring its velocity would be100 × Δvv  = Δpp× 100  =1004π=1004×3.14                   =7.96  ≈  8
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