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Q.

Given : The mass of electron is 9.11x 10^-31kg ,
Planck constant is 6.626x 10^-34 Js , the uncertainty involved in the measurement of velocity within a distance of 0.1 $\overset{0}{A}$ is

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a

$5.79 \times 10^{7} {ms}^{- 1}$

b

$5 .79 \times 10^{8} {ms}^{- 1}$

c

$5.79 \times 10^{6} {ms}^{- 1}$

d

$5 .79 \times 10^{5} {ms}^{- 1}$

answer is C.

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Detailed Solution

$Δx \cdot mΔv = \frac{h}{4 π}$
$0 .1 \times 10^{- 10} \times 9 .11 \times 10^{- 31} \times Δv = \frac{6 .626 \times 10^{- 34}}{4 \times 3 .14}$
$Δ v = \frac{6.626 \times 10^{- 34}}{0.1 \times 10^{- 10} \times 9.11 \times 10^{- 31} \times 4 \times 3.14}$
$= 5.79 \times 10^{6} m$

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