Uncertainty in position of an electron (m=9.1×10−28g) moving with a velocity of 3×104cm/s accurate upto 0.001% will be :
(Use h4π in uncertainty expression where h=6.626×10−27ergs)
7.68cm
5.79cm
1.93cm
3.84cm
A
1.93cm
B
5.79cm
C
7.68cm
D
3.84cm
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Solution
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According to Heisenbergs uncertainity principle,
Δx⋅mΔv=h4Π
so,Δx⋅Δv=h4Πm
Hence, product of uncertainity in position and velocity=h4πm
Here,m=9.1×10−28g,h=6.626×10−27Js
now, product of uncertainity in position and velocity=6.626×10−27/(4×3.14×9.1×10−28×0.3)
=(6.626×10−27)/(4×3.14×9.1×10−27×0.3)
=1.93cm
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