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Chemistry Question on Structure of atom

In an atom, an electron is moving with a speed of 600 m/s600\,m/s with an accuracy of 0.005%.0.005\%. Certainity with which the position of the electron can be located is (h=6.6?10−34kg m2 s−1h = 6.6 ? 10^{-34} kg\, m^2\,s^{-1} , mass of electron, em=9.1?10−kge_m = 9.1?10^{- kg} )

A

1.52?10−4m1.52 ? 10^{-4}m

B

5.10?10−3m5.10 ? 10^{-3}m

C

1.92?10−3m1.92 ? 10^{-3}m

D

3.84?10−3m3.84 ? 10^{-3}m

Answer

1.92?10−3m1.92 ? 10^{-3}m

Explanation

Solution

Δx.m Δv=h4π\Delta x.m\,\Delta v=\frac{h}{4\pi} Δx=h4π mΔv\Delta x=\frac{h}{4\pi\,m\Delta v} Δv=600×0.005100=0.03\Delta v=600\times\frac{0.005}{100}=0.03 ⇒Δx=6.625×10−344×3.14×9.1×10−31×0.03=1.92×10−3 m\Rightarrow \Delta x=\frac{6.625\times10^{-34}}{4\times3.14\times9.1\times10^{-31}\times0.03}=1.92\times10^{-3}\,m