Heisenberg's Uncertainty Principle

Details of Heisenberg's Uncertainty Principle 

All moving objects that we see around us e.g., a car, a ball thrown in the air etc., move along definite paths. Hence their position and velocity can be measured accurately at any instant of time. Is it possible for subatomic particle also?

As a consequence of dual nature of matter, Heisenberg, in 1927 gave a principle about the uncertainties in simultaneous measurement of position and momentum (mass × velocity) of small particles which is known as Heisenberg’s uncertainty principle

Heisenberg’s uncertainty principle states that “It is impossible to measure simultaneously the position and momentum of a small microscopic moving particle with absolute accuracy or certainty” i.e., if an attempt is made to measure any one of these two quantities with higher accuracy, the other becomes less accurate. The product of the uncertainty in position (Δx) and the uncertainty in the momentum (Δp = m.Δv where  m is the mass of the particle and Δv is the uncertainty in velocity) is equal to or greater than h/4π where h is the Planck’s constant.

Thus, the mathematical expression for the Heisenberg’s uncertainty principle is simply written as

            Δx . Δp ≥ h/4π

Explanation of Heisenberg’s uncertainty principle

    Suppose we attempt to measure both the position and momentum of an electron, to pinpoint the position of the electron we have to use light so that the photon of light strikes the electron and the reflected photon is seen in the microscope. As a result of the hitting, the position as well as the velocity of the electron is disturbed. The accuracy with which the position of the particle can be measured depends upon the wavelength of the light used. The uncertainty in position is ±λ. The shorter the wavelength, the greater is the accuracy. But shorter wavelength means higher frequency and hence higher energy. This high energy photon on striking the electron changes its speed as well as direction. But this is not true for macroscopic moving particle. Hence Heisenberg’s uncertainty principle is not applicable to macroscopic particles.

Solved example of Heisenberg’s uncertainty principle

Heisenberg’s uncertainty principle EXAMPLE-1

If the uncertainty in the position of an electron is 0.33 pm, what will be uncertainty in its velocity?

Solution:   

m/sec.

Heisenberg’s uncertainty principle EXAMPLE-2
 

Calculate the uncertainty in velocity of a ball of mass gms if the uncertainty in position is of the order of 1 A^o.

Solution:

Physical chemistry in class 11 consist of very fundamental chapters and need good attension always start from mole concept chapter and try to solve the questions based on mole it will help you to build a solid foundation in funda