(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?

An electron with initial kinetic energy $5.0$ eV encoun­ters a barrier with height $U_0$ and width $0.60$ nm. What is the transmission coefficient if (a) $U_0=7.0$ eV; (b) $U_0=9.0$ eV; (c) $U_0=13.0$ eV?

While undergoing a transition from the $n=1$ to the $n=2$ energy level, a harmonic oscillator absorbs a photon of wavelength $6.50$ $\mu$m. What is the wavelength of the absorbed photon when this oscillator undergoes a transition (a) from the $n=2$ to the $n=3$ energy level and (b) from the $n=1$ to the $n=3$ energy level?

(c) What is the value of $\sqrt{\left(k^{\prime }/m\right)}$, the angular oscillation frequency of the corresponding Newtonian oscillator?

(II) What is the speed of an electron after being accelerated from rest by 28,000 V?

Why is it important to know if your reference point is moving when analyzing the motion of an object in physics?