Question

An atom of neon has a radius rNe = 38. pm and an average speed in the gas phase at 25°C of 350.⁢/ms. Suppose the speed of a neon atom at 25°C has been measured to within 0.010%. Calculate the smallest possible length of box inside of which the atom could be known to be located with certainty. Write your answer as a multiple of rNe and round it to 2 significant figures. For example, if the smallest box the atom could be in turns out to be 42.0 times the radius of an atom of neon, you would enter "42.rNe" as your answer.

Answer 1

Answer:

                1.2* 10³ rNe.

Explanation:

Given speed of neon=350 m/s

Un-certainity in speed= (0.01/100) *350 =0.035 m/s

As per heisenberg uncertainity principle

              Δx*mΔv ≥$\frac{h}{4\pi }$     ..................(1)

  mass of neon atom    =$\frac{20*10^{-3} }{6.22*10^{-23} } =3.35*10^{-26} kg$

substituating the values in eq. (1)

        Δx =4.49*$10^{-8}$ m

In terms of rNe i.e 38 pm= 38*$10^{-12}$

               Δx=$\frac{4.49*10^{-8} }{38*10^{-12} }$

                   =0.118*$10^{4}$* (rNe)

                   =1.18*10³ rN

                   = 1.2* 10³ rNe.