Name: Dual Nature of Light and Matter
Uploaded: 2019-07-19
Duration: 7 min 31 s
Description: Light has a dual nature. It is both a wave and a particle. Explore this video about the wave and particle nature of light and the wavelength corresponding to...

Question

The effect of uncertainty principle is significant only for motion of microscopic particles and is negligible for the macroscopic particle. Justify the statement with the help of a suitable example.

Accepted Answer

The mathematical statement of the Heisenberg's Uncertainty Principle is given as, $∆ x . ∆ v \geq \frac{h}{4 πm}$ .

The effect of this principle is significant only in case of microscopic objects and is negligible in case of macroscopic object. For example, in an electron of mass $9.11 \times 10^{- 31} kg$ .
$∆ x . ∆ v = \frac{h}{4 πm} = \frac{6.626 \times 10^{- 34} Js}{4 \times 3.14 \times 9.11 \times 10^{- 31} kg} \approx 10^{- 4} m^{2} s^{- 1}$

It means that, if we want to find the exact location of the electron, with an uncertainty of $10^{- 8} m$ , then the uncertainty $∆ v$ in velocity is given by $\frac{10^{- 4} m^{2} s^{- 1}}{10^{- 8} m} = 10^{4} {ms}^{- 1}$ .

The value obtained is large enough so that the classical picture of electrons moving in Bohr's orbital (fixed) cannot hold good for it. The quantum mechanical model of atom deals with this fact.

However, for a macroscopic object of mass, say about a gram $(10^{- 3} kg)$ , then

$∆ x . ∆ v = \frac{h}{4 πm} = \frac{6.626 \times 10^{- 34} Js}{4 \times 3.14 \times 1 \times 10^{- 3} kg} \approx 10^{- 31} m^{2} s^{- 1}$

The value of $∆ x . ∆ v$ obtained is extremely small and is insignificant. Therefore, one may say that for macroscopic objects, the associated uncertainties are hardly of any real consequence.

The effect of uncertainty principle is significant only for motion of microscopic particles and is negligible for the macroscopic particle. Justify the statement with the help of a suitable example.

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