110年 - 110 國立臺北科技大學_碩士班招生考試_光電工程系碩士班：近代物理#102036

(1) What is the maximum wavelength of the incident radiation that could cause electrons to be released from the metal? (5%)

(2) If the wavelength of the incident radiation were changed to 288 nm, what would be the maximum kinetic energy of the emitted electrons? (5%)

2. A special kind of lightbulb emits monochromatic light of wavelength 630 nm. Electrical energy is supplied to it at the rate of 60 W, and the bulb is 93% efficient at converting that energy to light energy. How many photons are emitted by the bulb during its lifetime of 730 hours? (10%)

3. Consider a beam of 54-eV electrons directed at a nickel target. The potential energy of an electron that enters the target changes by 26 eV. Find the de Broglie wavelengths of the electrons outside and inside the target. (10%)

(1) What wavelengths can be emitted by the atom? (5%)

(2) What wavelengths can be absorbed by the atom? (5%)

(1) Please write down the stationary Schrodinger's equation for the particle. Clarify every symbol that you use in the equation.(10%)

(2) If this particle is confined in an infinite potential well of width a , that is,

Find the energy levels En of this particle and the corresponding normalized wavefunctions by solving the Schrodinger's equation. (15%)

(3) Following (2), if the particle is in a state , find the detectable energies and the corresponding probabilities. (10%)

(4) Suppose now the particle is moving in the following potential:

Show that the condition for the existence of at least one bound state of the particle is , where h is the Planck constant. (15%)

6. Find the minimum magnetic field needed for the (normal) Zeeman effect to be observed in a spectral line of 400-nm wavelength when a spectrometer whose resolution is 0.010 nm is used. (10%)

110年 - 110 國立臺北科技大學_碩士班招生考試_光電工程系碩士班：近代物理#102036

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