Question

In an atom, an electron is moving with a speed of 600m/s with an accuracy of 0.005%. What is the certainity with which the position of the electrons can be located? (h= 6.6*10-34 kg m2/s, mass of electron = 9.1*10-31 kg)

Answer 1

Answer:

1.9 x 10-5  will be the certainty.

Explanation:

Since, we know from the question that the velocity of the electron is =600m/s.

Also, the accuracy given is = 0.005%.

So, the uncertainty in the velocity will be given as = 600 x 5 /1000.

Which on solving we will get =  3000/1000

                                                 =  3 m/s.

Again we know that the Heisenberg uncertainty equation is ΔX * Δp = h/4π  where p is the momentum

So, to get the value of  ΔX we have.

ΔX = h/4π * mΔv

Now, putting the value we will get ΔX= 6.634 x10-34/ 4 x 3.14 x9.1 x 10-31 x 3

Which on solving we will get the value  ΔX to be = 1.9 x 10-5.  

Answer 2

Answer:

Explanation:

Uncertainty in velocity (ΔV)=0.005 x 600m/s / 100 = 0.03 m/s

According to Heisenberg's uncertainty principle:

(Δx) (mΔv) ≥ $\frac{h}{4\pi }$

or Δx ≥ h / 4πmΔv

≥(6.6×10−34Js) / 4 (3.14) (9.1×10−31kg) (0.030ms−1)

≥1.9×10−3m