Question

A ball is thrown straight up at $\mathbf{25}\mathbf{}\mathit{m}\mathit{s}\mathbf{-}\mathbf{1}$. Someone asks “Ignoring air resistance. What is the probability of the ball tunneling to a height of$\mathbf{}\mathbf{1000}\mathbf{}$$\mathit{m}$?” Explain why this is not an example of tunneling as discussed in this chapter, even if the ball were replaced with a small fundamental particle. (The fact that the potential energy varies with position is not the whole answer-passing through nonrectangular barriers is still tunnelirl8.)

Short answer

This is not an example of tunneling.

Step-by-step solution

Definition of quantum tunneling

The quantum phenomenon, in which a particle can penetrate a barrier and pass through it even though it is forbidden classically, is known as quantum tunneling.

Explanation and conclusion

In tunneling, we consider that the particle’s potential energy drops down to its original value after it has crossed the barrier and reached to the other side.

In the case given above, the potential energy of the ball increases by virtue of its height $(PE=mgh).$ And when it reaches the highest point, i.e., the point where the kinetic energy is zero and potential energy is maximum, everything beyond this point is classically forbidden. But the ball cannot go beyond and hence this case cannot be considered under quantum tunneling.