Explanation of Heisenberg’s Uncertainty Principle
Heisenberg’s Uncertainty Principle:
From Bohr’s atomic model, we know that an electron is a particle with a tiny mass revolving in a circular path, which remains in a specific energy level at a definite distance from the nucleus. Therefore, according to Bohr, the electron is a particle that possesses a definite momentum. However, according to de Broglie, an electron moves in a wave-like manner. Hence, in this state, it is impossible to determine both the position and momentum of an electron simultaneously and accurately.
As a result, if the position of the electron is determined accurately at any time, its momentum cannot be determined accurately; conversely, if the momentum of the electron is determined accurately, its position cannot be determined accurately.
In 1927, German scientist Werner Heisenberg presented a principle regarding the amount of error or uncertainty involved when the position and momentum of a particle are determined simultaneously. This is named after him as Heisenberg’s Uncertainty Principle.
“It is impossible to determine simultaneously and accurately both the position and momentum of a moving microscopic particle (such as an electron).”
Mathematical Explanation:
Let the error or uncertainty in determining the position of a microscopic particle = Δx
And the error or uncertainty in determining its momentum = Δp
Then, according to Heisenberg’s Uncertainty Principle, the product of the uncertainties in position and momentum is greater than or equal to the product of h/4π.
Since momentum uncertainty Δp = m·Δv (where m is the rest mass and Δv is the uncertainty in velocity), the equation can also be written as follows:
or, Δx · Δv ≥
The equation above is the mathematical expression of Heisenberg’s Uncertainty Principle.
Significance of the Equation: It can be inferred from this equation that when the uncertainty in position (Δx) is extremely small, the position can be determined accurately, but the uncertainty in momentum (Δp) becomes very large. Consequently, the momentum cannot be measured accurately. Conversely, when the uncertainty in momentum (Δp) is extremely small, the momentum can be determined accurately, but the uncertainty in position (Δx) becomes very large. As a result, the position cannot be measured accurately.
