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

Question

In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005 %. Certainity with which the position of the electron can be located is (h = 6.6 × 10−34 kg m2 s−1 , mass of electron, em = 9.1×10− kg ) (A) 1.52 × 10−4m (B) 5.10 × 10−3m (C) 1.92 × 10−3m (D) 3.84 × 10−3m

Tardigrade Admin · Accepted Answer

Δ x.m Δ v=(h/4π) Δ x=(h/4π mΔ v) Δ v=600×(0.005/100)=0.03 ⇒ Δ x=(6.625×10-34/4×3.14×9.1×10-31×0.03)=1.92×10-3 m

Q. In an atom, an electron is moving with a speed of $600 m / s$ with an accuracy of $0.005%.$ Certainity with which the position of the electron can be located is ( $h = 6.6 \times 1 0^{- 34} k g m^{2} s^{- 1}$ , mass of electron, $e_{m} = 9.1 \times 1 0^{- k g}$ )

$1.52 \times 1 0^{- 4} m$

$5.10 \times 1 0^{- 3} m$

$1.92 \times 1 0^{- 3} m$

$3.84 \times 1 0^{- 3} m$

$Δ x . m Δ v = \frac{h}{4 π}$
$Δ x = \frac{h}{4 π m Δ v}$
$Δ v = 600 \times \frac{0.005}{100} = 0.03$
$\Rightarrow Δ x = \frac{6.625 \times 1 0 ^{- 34}}{4 \times 3.14 \times 9.1 \times 1 0 ^{- 31} \times 0.03} = 1.92 \times 1 0^{- 3} m$

Q. In an atom, an electron is moving with a speed of 600m/s with an accuracy of 0.005%. Certainity with which the position of the electron can be located is (h=6.6×10−34kgm2s−1 , mass of electron, em​=9.1×10−kg )

1.52×10−4m

5.10×10−3m

1.92×10−3m

3.84×10−3m