Question

Select True or False for the following statements about Heisenberg's Uncertainty Principle. True False It is not possible to measure simultaneously the x and y positions of a particle exactly.
True False It is not possible to measure simultaneously the x and y momentum components of a particle exactly.
True False It is not possible to measure simultaneously the z position and the z momentum component of a particle exactly.

Answer 1

Answer:

Statement 1) False

Statement 2) False

Statement 3) True

Explanation:

The uncertainty principle states that " in a physical system certain quantities cannot be measured with random precision no matter whatever the least count of the instrument is" or we can say while measuring simultaneously the position and momentum of a particle the error involved is

$P\cdot\delta x\geq \frac{h}{4\pi }$

Thus if we measure x component of momentum of a particle with 100% precision we cannot measure it's position 100% accurately as the error will be always there.

Statement 1 is false since measurement of x and y positions has no relation to uncertainty.

Statement 2 is false as both the momentum components can be measured with 100% precision.

Statement 3 is true as as demanded by uncertainty principle since they are along same co-ordinates.