12.2.4 Exploring quantum tunneling

• What is quantum tunneling?

  Passing through energy barriers
• Match the behavior with the physical principle:

  Classical physics ↔️ Particle cannot pass through barrier if energy < barrier height

  Quantum mechanics ↔️ Particle can tunnel through barrier even if energy < barrier height
• The Heisenberg uncertainty principle states that there is a fundamental limit on the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously.
• The constant h in the Heisenberg uncertainty principle represents Planck's constant.

  True
• Outside the potential energy barrier, the probability amplitude of a particle is independent of the barrier thickness.


  True
• Inside the potential energy barrier, the probability amplitude of a particle undergoing quantum tunneling exponentially decays
• Exponential decay in quantum tunneling explains why wide barriers are difficult to tunnel through
• Arrange the variables of the WKB formula in the correct order.

  1️⃣ Barrier boundaries (a and b)

  2️⃣ Particle mass (m)

  3️⃣ Potential energy function (V(x))

  4️⃣ Particle energy (E)

  5️⃣ Planck's constant (h)
• Higher energy particles have a greater probability of tunneling
• What is the mathematical expression for the Heisenberg uncertainty principle?

  $\Delta x \Delta p \geq \frac{h}{4\pi}$
• Inside the potential energy barrier, what happens to the probability amplitude of a particle undergoing quantum tunneling?

  It decays exponentially
• The Heisenberg uncertainty principle arises from the wave-like nature of particles.

  True
• What primarily affects the exponential decay of probability amplitude inside the potential energy barrier?

  Barrier thickness
• The thicker the potential energy barrier, the more likely quantum tunneling becomes.

  False
• What is the WKB approximation used to calculate in quantum tunneling?

  Tunneling probability
• The tunneling probability is highest when the barrier is low and narrow
• What happens to a particle approaching a potential energy barrier in classical physics if its energy is less than the barrier height?

  It cannot pass through
• Quantum tunneling is used in technologies like scanning tunneling microscopes.


  True
• The probability amplitude inside the barrier decays faster for barriers that are thicker.
• The probability amplitude outside the barrier oscillates.


  True
• How does the probability amplitude change inside the potential energy barrier?

  Exponential decay
• Higher potential energy barriers result in a lower tunneling probability.


  True
• Match the application of quantum tunneling with its description.

  Scanning Tunneling Microscopes (STMs) ↔️ Allows atomic-level imaging

  Flash Memory ↔️ Stores data using electron tunneling

  Nuclear Fusion in Stars ↔️ Enables fusion despite repulsion