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If uncertainty in the position of the electron is zero, then its uncertainty in momentum will be:
1. h / 2π
2. h / 4π
3. zero
4. infinity

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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.

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