Question

Which of the following statements are true according to the uncertainty principle? A. It is impossible to simultaneously determine both the energy and the momentum of a particle with arbitrary accuracy. B. It is impossible to determine a particle's energy with arbitrary accuracy in a finite amount of time. C. It is impossible to simultaneously determine both the position and the momentum of a particle with arbitrary accuracy. D. It is impossible to measure the position of a particle with arbitrary accuracy in a finite amount of time. E. It is impossible to simultaneously measure both the energy and position of a particle with arbitrary accuracy.

Answer 1

Answer and Explanation: Heisenberg's Uncertainty Principle states that if the position of the particle is known, its momentum is unknown and vice-versa.

So, it is impossible to determine both the position and the momentum of a particle with arbitrary accuracy.

Answer 2

The statement, " It is impossible to simultaneously determine both the position and the momentum of a particle with arbitrary accuracy" is correct. Hence, option (c) is correct.

The given problem is based on the Heisenberg's uncertainty principle. As per the Heisenberg's uncertainty principle, "It is not possible to obtain both the momentum and position of particles at same time, if one is obtained with full certainty then other comes uncertain". And the expression for the Heisenberg's principle is,

$\Delta x \times \Delta p \geq \dfrac{h}{4\pi}$

Here,

$\Delta x$ is the uncertainty in position.

$\Delta p$  is the uncertainty in momentum.

h is the Planck's constant.

So, as per the above definition the statement, " It is impossible to simultaneously determine both the position and the momentum of a particle with arbitrary accuracy" is justified.

Thus, we can conclude that the statement, " It is impossible to simultaneously determine both the position and the momentum of a particle with arbitrary accuracy" is correct. Hence, option (c) is correct.

Learn more about the Heisenberg's uncertainty principle here:

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