Structure of the atom：練習問題

In Rutherford’s alpha-particle scattering experiment, what was the primary observation that led to the conclusion that the nucleus is extremely small and carries a positive charge?

A hydrogen atom is initially in the first excited state (\(n=2\)). Given that the energy of the \(n\)-th level is \(E_n = -\frac{13.6}{n^2}\) eV, which of the following statements is correct?

A specific series of spectral lines in the hydrogen spectrum is produced when electrons transition from higher energy levels to the \(n = 3\) level. What is the ratio of the longest wavelength to the shortest wavelength in this series?

Which of the following statements about the Bohr model of the hydrogen atom is correct?

An ion of an isotope is represented by the symbol \({}_{15}^{31}\text{P}^{3-}\). Which of the following correctly identifies the number of protons, neutrons, and electrons in this ion?

What do the atomic number and mass number represent in the structure of an atom?

An atom of carbon has an atomic number of 6 and a mass number of 14. Determine the number of protons, neutrons, and electrons in a neutral atom of this carbon isotope.

In Rutherford's scattering experiment, an alpha particle (charge \(+2e\)) is fired head-on at a silver nucleus (atomic number \(Z=47\)) with an initial kinetic energy of \(8.0 \text{ MeV}\). Calculate the distance of closest approach for this collision.
(Given: \(1 \text{ MeV} = 1.6 \times 10^{-13} \text{ J}\), \(\frac{1}{4\pi\epsilon_0} = 9.0 \times 10^9 \text{ N m}^2 \text{ C}^{-2}\), \(e = 1.6 \times 10^{-19} \text{ C}\))

The structure of the atom has been described by various scientific models. One of the most important was the model proposed by Ernest Rutherford.

(a) Describe the structure of a neutral atom based on Rutherford’s model, including the location and charge of the nucleus and the position of the electrons.

(b) Define the terms atomic number and mass number.

(c) A nuclide is represented by the symbol \({}_{13}^{27}\text{Al}\). Determine the number of protons and the number of neutrons in this atom.

Consider the Paschen series of the hydrogen emission spectrum, which corresponds to electron transitions from higher energy levels to the \( n=3 \) level.

(a) Calculate the energy of the photon emitted when an electron transitions from the \( n=5 \) level to the \( n=3 \) level in eV.
(b) Determine the wavelength of this photon and identify which part of the electromagnetic spectrum it belongs to.
(c) Explain why the lines in the Paschen series are generally closer together than those in the Balmer series.

(Given: \( E_n = -\frac{13.6}{n^2} \text{ eV} \), \( h = 6.63 \times 10^{-34} \text{ J s} \), \( c = 3.00 \times 10^8 \text{ m/s} \))