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Chemistry Question on Structure of atom

The uncertainty in momentum of an electron is 1×10−5kgm/s.1\times 10^{-5} kg m/s. The uncertainty in its position will be (Given, h=6.62×10−34kgm2/s)h = 6.62 \times 10^{-34} kg m^2/s)

A

1.05×10−28m1.05 \times 10^{-28} m

B

1.05×10−26m1.05 \times 10^{-26} m

C

5.27×10−30m5.27 \times 10^{-30} m

D

5.25×10−28m5.25 \times 10^{-28} m

Answer

5.27×10−30m5.27 \times 10^{-30} m

Explanation

Solution

The uncertainty in the momentum of an electron is 1 × 10-5 kgm/s

According to the uncertainty principle, it is impossible to precisely identify a particle's position and momentum at the same time. Position and momentum always produce a result that is greater than h/4. The Heisenberg Uncertainty Principle's formula is as:
Δp×Δx≥h4π\Delta p \times \Delta x \ge\frac{h}{4\pi}

Here, h is the Planck’s constant ( 6.62607004 × 10-34 m2 kg / s)

Δp is the uncertainty in momentum

Δx is the uncertainty in position

So, Δp = 1 × 10-5 kgm/s
So, the Uncertainty in position(Δx) will be-
\hspace15mm \Delta p=1\times10^{-5} kg m/s
1×10−5×Δx=6.62×10−344×2271\times10^{-5}\times \Delta x=\frac{6.62 \times 10^{-34}}{4\times\frac{22}{7}}
                   Δx=6.62×10−34×710−5×4×22\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \Delta x=\frac{6.62 \times 10^{-34}\times 7}{10^{-5}\times 4\times 22}
=5.265×10−30m= 5.265 \times 10^{-30} m
≈5.27×10−30m\approx 5.27 \times 10^{-30} m

Uncertainty is a basic characteristic of nature.

  • We, therefore, came to the conclusion that it is challenging to precisely and concurrently identify a particle's location and momentum.
  • Therefore, the concepts of precise location and precise velocity are useless.
  • This concept won't be revealed by ordinary scientific experience. It is because it is easy to determine an object's velocity and position.
  • This is due to the fact that the implied uncertainty of this concept for typical things is too modest to be seen.
  • Because of this, the uncertainty in location and velocity is more than or equal to h, a very, very tiny physical quantity.
  • Because of this, this product of uncertainty will only have a very minor impact on atoms and subatomic particles.

Discover more from this chapter:Structure of Atom