An electron in a one­-dimensional box has ground ­state energy $2.00$ eV. What is the wavelength of the photon absorbed when the electron makes a transition to the second excited state?

Consider a wave function given by $\psi \left(x\right)=Asinkx$, where $k=2\pi /\lambda$ and $A$ is a real constant.

(a) For what values of $x$ is there the highest probability of finding the particle described by this wave function? Explain.

(b) For which values of $x$ is the probability zero? Explain.

(a) Find the lowest energy level for a particle in a box if the particle is a billiard ball ($m=0.20$ kg) and the box has a width of $1.3$ m, the size of a billiard table. (Assume that the billiard ball slides without friction rather than rolls; that is, ignore the rotational kinetic energy.)

(b) Since the energy in part (a) is all kinetic, to what speed does this correspond? How much time would it take at this speed for the ball to move from one side of the table to the other?

A particle in a box is a billiard ball ($m = 0.20$ kg) and the box has a width of $1.3$ m, the size of a billiard table. (Assume that the billiard ball slides without friction rather than rolls; that is, ignore the rotational kinetic energy.) What is the difference in energy between the $n=2$ and $n=1$ levels? Are quantum­ mechanical effects important for the game of billiards?

A proton is in a box of width $L$. What must the width of the box be for the ground­-level energy to be $5.0$ MeV, a typi­cal value for the energy with which the particles in a nucleus are bound? Compare your result to the size of a nucleus — that is, on the order of ${10}^{-14}$ m.

(a) Find the excitation energy from the ground level to the third excited level for an electron confined to a box of width $0.360$ nm.

(b) The electron makes a transition from the $n=1$ to $n=4$ level by absorbing a photon. Calculate the wave­length of this photon.

An electron is in a box of width $3.0\times {10}^{-10}$ m. What are the de Broglie wavelength and the magnitude of the momentum of the electron if it is in (a) the $n=1$ level; (b) the $n=2$ level; (c) the $n=3$ level? In each case how does the wavelength compare to the width of the box?

An electron is in a box of width 3.0*10^-10 m. What are the de Broglie wavelength and the magnitude of the momentum of the electron if it is in (a) the n = 1 level; (b) the n = 2 level; (c) the n = 3 level? In each case how does the wavelength compare to the width of the box?

(a) An electron with initial kinetic energy $32$ eV encoun­ters a square barrier with height $41$ eV and width $0.25$ nm. What is the probability that the electron will tunnel through the barrier?

(b) A proton with the same kinetic energy encounters the same barrier. What is the probability that the proton will tunnel through the barrier?