Heisenberg Uncertainty Principle

The uncertainty principle also called Heisenberg uncertainty principle. Bohr theory has explained that the electron present in a particular energy level cannot lose the energy of its own. It can do so when it jumps from a higher energy level to the lower energy level. Thus, in its stationary state, the electron keep on revolving in the same circular orbit and does not come close to the nuclear as suspected by the radiation theory. This accounts for the stability of an atom.

Must Read: Bohr Theory in Detail.

The serious blow to Bohr’s theory came from certain new principles such as de Broglie’s relationship and Heisenberg principle. According to Bohr’s theory, an electron follows a fixed circular path with definite energy and thus, both its position and direction can be well defined. However, these principles stated that the path of the electron is not definite. It is of probable nature. Moreover, an electron has both wave and particle nature according to these.

Heisenberg Uncertainty Principle

We have seen that according to de Broglie relationship, a microscopic particle such as an electron has both wave and particle characters. In 1927, Werner Heisenberg a German physicist pointed out that we can never measure simultaneously the exact position and the exact momentum (velocity) of the microscopic particles which are as small as electrons. This is known as uncertainty principle.Heisenberg Uncertainty Principle

Heisenberg Uncertainty Principle Definition

It states as follows:

It is not possible to measure simultaneously the position and the momentum of a microscopic particle with absolute accuracy or certainty.

Heisenberg Uncertainty Principle Equation

Alternatively, the principle may also be stated as:

The product of the uncertainty in the position and uncertainty in the momentum of a microscopic particle is always constant and is equal to or greater than h/4π.

Δp. Δx ≥ h/4π(Constant)

  • Δx = Uncertainty in measuring exact position.
  • Δmv or Δp = Uncertainty in measuring exact momentum or velocity.

Heisenberg Uncertainty Principle Formula

Mathematically,

  •  Δx.Δp=h/4π.
  • or  Δx.mΔv =h/4π

Heisenberg Uncertainty Principle Explanation

From the above relationship, it is evident that

(i) If Δx is very small: The position of the microscopic particle can be measured accurately (certainty in position will be very large). But Δp will be very large (since the product of Δx and Δp is constant) which means that momentum or velocity of the particle cannot be measured with accuracy.

(ii) If Δp is very small: The momentum or velocity of the microscopic particle can be measured accurately. But uncertainty will be introduced in measuring its position.

(iii) If Δx is zero: The position can be located with absolute accuracy but in this case, Δp will be infinity which means that the momentum or velocity of the microscopic particle cannot be measured at all.

Significance of Uncertainty Principle

We know that an object can be seen by illuminating it with light rays consisting of photons. When a beam of light reflected from the surface of the object reaches our eye or any measuring device, the object will become visible.

According to the principle of optics, the accuracy with which a particle can be located depends upon the wavelength of the light used. The uncertainty in position is ± λ.

Shorter the wavelength, the greater will be accuracy in measuring the position. But shorter wavelength will mean high frequency and high energy of the striking photons.

 Heisenberg Uncertainty Principle

 

These are likely to displace the electrons from their normal path and both the speed as well as direction are likely to change. We can visualize the same from another angle. Shorter wavelength implies – higher momentum      (λ = h/p or p = h/λ).

This means that the striking photons will impart greater momentum to the electrons at the time of impact. This will lead to greater uncertainty in velocity.

In case momentum is decreased, then wavelength will increase which means greater uncertainty in measuring the position. Thus, both the exact position and momentum (velocity) for such particles cannot be measured simultaneously. If we try to have a control on one we lose control over the other and vice versa. In general, we can also say that

We cannot see a microscopic particle like electron without disturbing it.

This is about the Uncertainty Principle.

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