Question

Which of the following are valid consequences or applications of uncertainty principle?
• Non-Existence of electron inside the nucleus.
• Particles must have minimum (Ground state) energy.
• It defines the probabilistic nature (Orbital) of electrons in atoms.
• It limits the precision with which we can measure a football's position and speed simultaneously. Choose the correct answer from the options given below:

• A. B & D Only
• B. A, B & D Only
• C. A, B & C Only
• D. A, B, C & D Only

Hint:

Uncertainty principle explains:
• Electron orbitals
• Zero point energy
• Why electrons cannot stay inside nucleus

Answer 1

The Correct Option is C

Concept: Heisenberg uncertainty principle states that the exact position and momentum of a particle cannot be determined simultaneously with absolute precision. Mathematically: :contentReference[oaicite:0]{index=0} This principle has several important consequences in quantum mechanics and atomic physics.

Step 1: Analyze Statement A. Statement A says: “Non-existence of electron inside the nucleus” Suppose an electron were confined inside the nucleus. Since nuclear radius is extremely small: \[ \Delta x \approx 10^{-15}\ \text{m} \] By uncertainty principle: \[ \Delta p \geq \frac{h}{4\pi \Delta x} \] Thus momentum uncertainty becomes extremely large. This would imply:
• Very large kinetic energy for electron Such enormous energy is inconsistent with observed nuclear stability. Therefore electrons cannot exist inside nucleus permanently. Hence Statement A is correct.

Step 2: Analyze Statement B. Statement B says: “Particles must have minimum (Ground state) energy” If a particle had exactly zero energy:
• Momentum would become zero.
• Position and momentum would both become definite. This violates uncertainty principle. Therefore every quantum particle must possess: \[ \boxed{ \text{Minimum non-zero energy} } \] called zero point or ground state energy. Hence Statement B is correct.

Step 3: Analyze Statement C. Statement C says: “It defines the probabilistic nature (Orbital) of electrons in atoms” Because exact position and momentum cannot be simultaneously determined:
• Electrons cannot move in sharp definite paths.
• Electrons are described by probability distributions. Thus orbitals arise naturally from uncertainty principle and wave mechanics. Hence Statement C is correct.

Step 4: Analyze Statement D carefully. Statement D says: “It limits the precision with which we can measure a football's position and speed simultaneously” Technically uncertainty principle applies to all objects. However:
• For macroscopic objects like footballs, Planck's constant is extremely small.
• Resulting uncertainty is practically negligible. Thus this is not considered a meaningful practical consequence/application in classical systems. Hence Statement D is not taken as correct in this context.

Step 5: Determine the correct combination. Correct statements are: \[ A,\ B,\ C \] Incorrect statement: \[ D \] Therefore: \[ \boxed{ A,\ B\ \&\ C\ \text{Only} } \]

Step 6: Choose the correct answer. Hence the correct option is: \[ \boxed{(3)} \] Final Conclusion: Valid consequences/applications of uncertainty principle are:
• Non-existence of electron inside nucleus
• Existence of minimum ground state energy
• Probabilistic electron orbitals Hence, the correct answer is: \[ \boxed{(3)} \]