Electromagnetic radiation and quantum phenomena：練習問題

A large sample of atoms of a specific element is excited to the fourth energy level ( \( n = 4 \)). If electrons can transition between any of the discrete energy levels down to the ground state ( \( n = 1 \)), what is the maximum number of different spectral lines that could be observed in the emission spectrum?

A particle with charge \(Q\) and mass \(m\) is accelerated from rest through a potential difference \(V\). Its final de Broglie wavelength is \(\lambda\). If a second particle with charge \(2Q\) and mass \(8m\) is accelerated through the same potential difference, what is its de Broglie wavelength in terms of \(\lambda\)?

An atom has three discrete energy levels: the ground state \(E_0\), and two excited states \(E_1\) and \(E_2\). When an electron transitions from \(E_2\) to \(E_1\), a photon of wavelength \(\lambda_{21}\) is emitted. When an electron transitions from \(E_1\) to \(E_0\), a photon of wavelength \(\lambda_{10}\) is emitted. Which expression correctly gives the wavelength \(\lambda_{20}\) emitted during a transition from \(E_2\) to \(E_0\)?

Which of the following observations in the photoelectric effect experiment provides the most direct evidence that electromagnetic radiation behaves as a stream of discrete energy packets rather than a continuous wave?

The threshold frequency for a certain metal is \(f_0\). When light of frequency \(3f_0\) is incident on the metal, the maximum kinetic energy of the photoelectrons is \(K\). If light of frequency \(4f_0\) is used, what will be the new maximum kinetic energy of the photoelectrons?

Show that the de Broglie wavelength \( \lambda_e \) of an electron with kinetic energy \( E_k \) can be expressed as \( \lambda_e = \sqrt{\frac{h \lambda_p}{2mc}} \), where \( \lambda_p \) is the wavelength of a photon having the same energy \( E_k \), \( m \) is the mass of the electron, and \( c \) is the speed of light in a vacuum.

A beam of electrons is directed at a thin graphite film, producing a diffraction pattern of concentric rings on a fluorescent screen. Explain how the appearance of the pattern changes when the speed of the incident electrons is increased.

Ultraviolet radiation of wavelength \( 180 \text{ nm} \) is incident on a metal surface. The maximum de Broglie wavelength of the emitted photoelectrons is found to be \( 1.50 \times 10^{-9} \text{ m} \). Calculate the work function of the metal in electronvolts (\( \text{eV} \)).

A thermal neutron has a velocity of \( 2.20 \times 10^3 \text{ m s}^{-1} \).

(a) Calculate the de Broglie wavelength of this neutron.

(b) State why a macroscopic object, such as a baseball moving at the same speed, would not demonstrate observable wave-like properties such as diffraction.

Fluorescent tubes use both electron collisions and photon emission to produce visible light.

(a) Describe the process that occurs when high-speed electrons pass through the mercury vapor in the tube.

(b) Explain why the mercury atoms emit ultraviolet photons rather than visible light photons during de-excitation.

(c) Explain the role of the phosphor coating on the inside of the glass and how it converts UV radiation into visible light.