Correct Answer - Option 4 : infinity
Concept:
Heisenberg’s Uncertainty Principle:
- It states that it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron.
- Mathematically, it can be given as
\({\rm{\Delta }}x \times {\rm{\Delta }}{p_x} \ge \frac{h}{{4\pi }}\)
∆x is uncertainty in position, ∆px is uncertainty in momentum at position x.
Explanation:
Now, it is given that uncertainty in momentum is zero.
∆px = 0
But, by the uncertainty principle
\({\rm{\Delta }}x \times {\rm{\Delta }}{p_x} \ge \frac{h}{{4\pi }}\)
\(\implies {0} \times {\rm{\Delta }}{x} \ge \frac{h}{{4\pi }}\)
\(\implies {\rm{\Delta }}{x} \ge \frac{h}{{4\pi \times 0 }} \)
Now anything divided by zero is infinity. So, ∆x is infinity.
So, infinity is the correct answer.