Solveeit Logo
Login

Question

Question: According to Heisenberg’s uncertainty principle, the product of uncertainties in position and veloci...

According to Heisenberg’s uncertainty principle, the product of uncertainties in position and velocities for an electron of mass 9.1×10−31kg9.1 \times 10^{- 31}kg is

A

2.8×10−3m2s−12.8 \times 10^{- 3}m^{2}s^{- 1}

B

3.8×10−5m2s−13.8 \times 10^{- 5}m^{2}s^{- 1}

C

5.8×10−5m2s−15.8 \times 10^{- 5}m^{2}s^{- 1}

D

6.8×10−6m2s−16.8 \times 10^{- 6}m^{2}s^{- 1}

Answer

5.8×10−5m2s−15.8 \times 10^{- 5}m^{2}s^{- 1}

Explanation

Solution

Given that mass of electron =9.1×10−31kg= 9.1 \times 10^{- 31}kg

Planck’s constant =6.63×10−34kgm2s−1= 6.63 \times 10^{- 34}kgm^{2}s^{- 1}

By using Δx×Δp=h4π\Delta x \times \Delta p = \frac{h}{4\pi}; Δx×Δv×m=h4π\Delta x \times \Delta v \times m = \frac{h}{4\pi}

Where: Δx\Delta x = uncertainity in position

Δv\Delta v = uncertainity in velocity

Δx×Δv=h4π×m\Delta x \times \Delta v = \frac{h}{4\pi \times m}

=6.63×10−344×3.14×9.1×10−31= \frac{6.63 \times 10^{- 34}}{4 \times 3.14 \times 9.1 \times 10^{- 31}} =5.8×10−5m2s−1= 5.8 \times 10^{- 5}m^{2}s^{- 1}.