Q.

Uncertainty in position of an electron (mass = 9.1 x 10-28 g) moving with a velocity of 3 x 104 cm/s accurate upto 0.001% will be (use h/4π in uncertainty expression where h = 6.626 xl0-27 erg-second).

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a

1.93 cm

b

3.84 cm

c

7.68 cm

d

5.76 cm

answer is A.

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Detailed Solution

Given mass of an electron(m) = 9.1 x l0-28 g' 
Velocity of electron (v) = 3 x lO4cm/s;
Accuracy in velocity = 0.00l% = 0.001100;
Actual velocity of the electron
(Δv)=3×104×0.001100=0.3cm/s
Planck's constant (h) = 6.626x10-27 erg-sec.
 Uncertainty in the position of the electron
(Δx)=h4πmΔv=6.626×1027×74×22×9.1×1028×0.3=1.93cm

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