電子與原子的碰撞：練習題

Which statement correctly describes the process of ionisation when an electron collides with a neutral atom?

A fluorescent tube operates by collisions of electrons with mercury atoms. Which statement correctly describes the primary process occurring when electrons strike mercury atoms in the tube?

An atom has an ionisation energy of \(15.6 \text{ eV}\). It has three discrete excitation energy levels above the ground state at \(E_1 = 4.0 \text{ eV}\), \(E_2 = 6.5 \text{ eV}\), and \(E_3 = 9.8 \text{ eV}\). An electron with kinetic energy \(10.0 \text{ eV}\) collides with this atom, which is initially in its ground state. Assuming the collision is inelastic but does not cause ionisation, what is the maximum possible kinetic energy of the electron immediately after the collision?

The first excitation energy level of a specific atom is \(4.9 \text{ eV}\). What is the minimum kinetic energy, in Joules, an electron must possess to excite this atom from its ground state?

Elementary charge, \(e = 1.60 \times 10^{-19} \text{ C}\).

An X-ray tube produces a continuous spectrum of X-rays. If the accelerating voltage across the tube is doubled and the tube current is halved, what happens to the minimum wavelength (\( \lambda_{\text{min}} \)) of the produced X-rays?

Distinguish between the processes of excitation and ionisation of an atom caused by collision with an electron, referencing the final state of the electron involved.

In a fluorescent tube, UV photons are emitted when excited mercury atoms de-excite. If the energy difference between two specific energy levels in a mercury atom is \(4.9 \text{ eV}\), calculate the frequency of the UV photon emitted during this transition. (Use \(h = 6.63 \times 10^{-34} \text{ J s}\) and \(1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}\)).

Explain why the light emitted by excited gases consists of discrete line spectra rather than a continuous spectrum, relating this phenomenon to the energy structure of atoms.

An energy level diagram for a simplified atom shows the following discrete energy levels:
Ground state (\(n=1\)): \(-15.0 \text{ eV}\)
First excited state (\(n=2\)): \(-6.0 \text{ eV}\)
Second excited state (\(n=3\)): \(-3.0 \text{ eV}\)
The ionisation energy for this atom is \(0 \text{ eV}\).

(a) Calculate the frequency of the photon emitted when an electron undergoes a transition from the \(n=3\) level to the \(n=2\) level.

(b) Determine the shortest possible wavelength of radiation that can be emitted by this atom.

(c) Explain how these discrete energy levels and the resulting line spectra provide evidence for the existence of discrete energy states within atoms.

(Use: Planck constant, \(h = 6.63 \times 10^{-34} \text{ J s}\); Speed of light, \(c = 3.00 \times 10^8 \text{ m/s}\); Elementary charge, \(e = 1.60 \times 10^{-19} \text{ C}\))

The energy levels (relative to the ground state) of a hypothetical atom are given by \(E_n = \frac{A}{n^2}\), where \(A = -12.0 \text{ eV}\) and \(n\) is the principal quantum number (\(n=1\) for the ground state). Ionisation corresponds to \(E_n = 0\).

(a) Calculate the energy of the electron in the ground state (\(n=1\)) and the first excited state (\(n=2\)), stating your answers in electron volts.

(b) An electron beam is used to excite these atoms. Determine the minimum accelerating potential difference required for the electrons to excite an atom from its ground state to the \(n=3\) level.

(c) If an atom transitions from the \(n=3\) state back to the ground state (\(n=1\)) by emitting a single photon, calculate the wavelength of the emitted radiation.

(Use: Planck constant, \(h = 6.63 \times 10^{-34} \text{ J s}\); Speed of light, \(c = 3.00 \times 10^8 \text{ m/s}\); Elementary charge, \(e = 1.60 \times 10^{-19} \text{ C}\))