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QJEEM06Ch0b75: JEE Main 2006 Chemistry - Class 11 JEEM06Ch0b75 Solution: Uncertainty in the position of an electron (mass = 9.1 × 10 -31 …

Uncertainty in the position of an electron (mass = 9.1

\times

10^-31 kg) moving with a velocity 300 ms^-1, accurate upto 0.001% will be (h = 6.63

\times

10^-34 Js)

Step-by-Step Verified Solution

% error in velocity =

\frac{Δ V}{V} \times 100

∴

0.001 =

\frac{Δ V}{300} \times 100

\Rightarrow

Δ

V = 3

\times

10^-3

According to Heisenberg uncertainty principle,

Δ x . m Δ V \geq \frac{h}{4 π}

\Rightarrow

Δ x = \frac{h}{4 π m Δ V}

\Rightarrow

Δ x = \frac{6.63 \times 10^{- 34}}{4 \times 3.14 \times 9.1 \times 10^{- 31} \times 3 \times 10^{- 3}}

= 1.92

\times

10^-2 m