Structure Of The Atom

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课程笔记

Rutherford's Gold Foil Experiment

Rutherford's gold foil experiment provided evidence for the structure of the atom by firing high-energy α particles at a thin gold foil and detecting the angles of deflection.
The apparatus consisted of: a source of α particles in a lead container, a thin gold foil, a movable detector, and an evacuated chamber.
The lead container produced a collimated beam of α particles because α particles are absorbed by lead, so a narrow hole allowed a concentrated beam to escape.
The gold foil had to be extremely thin (about 10⁻⁶ m) because a thicker foil would stop the α particles completely; gold was chosen for its malleability.
The evacuated chamber prevented α particles from colliding with air molecules, as α particles are highly ionising and travel only about 5 cm in air.
Observations: most α particles passed straight through (atom is mostly empty space); some deflected through small angles <10° (positive nucleus at centre); a small number deflected back >90° (nucleus is extremely small and contains most mass and charge).
Conclusion: atoms consist of a small, dense, positively charged nucleus surrounded by negatively charged electrons; the atom is about 100,000 times larger than the nucleus.

Nuclear Notation

Atoms are made of three subatomic particles: protons, neutrons, and electrons.
Protons and neutrons are found in the nucleus, while electrons orbit the nucleus.
Charge can be expressed in coulombs (C) or units of elementary charge (e); mass can be expressed in kilograms (kg) or atomic mass units (u).
Proton: charge +1.60 × 10⁻¹⁹ C (+1e), mass 1.673 × 10⁻²⁷ kg (1.007276 u).
Neutron: charge 0, mass 1.675 × 10⁻²⁷ kg (1.008665 u).
Electron: charge −1.60 × 10⁻¹⁹ C (−1e), mass 9.109 × 10⁻³¹ kg (0.000549 u).
A nucleus is described using Z^A X notation: A is the nucleon (mass) number (total protons + neutrons) and Z is the proton (atomic) number (total protons).

Nuclide notation

Emission & Absorption Spectra

Atomic spectra are observed when atoms emit or absorb light of certain wavelengths, providing evidence that electrons can only transition between discrete energy levels.
Emission spectra are produced by heating a low-pressure gas: electrons are excited to higher levels, then emit photons when they transition back down, producing coloured lines on a black background.
Absorption spectra are produced by passing white light through a cool, low-pressure gas: photons with the exact energy required to excite electrons are absorbed, producing dark lines on a coloured background.
The dark lines in an absorption spectrum correspond to the same wavelengths as the bright lines in the emission spectrum of the same element.
Each element produces a unique pattern of spectral lines, so elements can be identified by their atomic spectrum (like a fingerprint).
Examples: hydrogen has strong red lines at 656 nm; sodium produces yellow lines at 589 nm; mercury has most lines below 450 nm, giving blue light.
In a fluorescent tube, an electrical discharge excites electrons in vapourised atoms; when electrons return to the ground state, they emit specific wavelengths of light.

Photon Energy

A photon is defined as a massless "packet" or "quantum" of electromagnetic energy; energy is transferred in discrete packets, not continuously.
Electrons in an atom occupy certain energy levels; they occupy the lowest possible energy level (ground state) for stability.
Excitation: an electron moves to a higher energy level by absorbing a photon; the atom is in an excited state.
De-excitation: an electron moves to a lower energy level by emitting a photon.
Ionisation: an electron is removed from an atom; the ionisation energy is the minimum energy required to remove an electron from the ground state.
Energy levels are represented as horizontal lines: the bottom line (most negative energy) is the ground state, lines above are excited states, and the top line (0 V or infinity) represents the ionisation energy.
Photon energy is calculated using E = hf or E = hc/λ, where h = Planck's constant (J s), c = speed of light (m s⁻¹), f = frequency (Hz), λ = wavelength (m).
The energy difference between two levels is ΔE = hf = E₂ − E₁; the larger the energy difference, the shorter the wavelength.

Rutherford Scattering & Nuclear Radius

The nuclear radius R depends on the nucleon number A: R = R₀ A^(1/3), where R₀ = 1.20 × 10⁻¹⁵ m is the Fermi radius (radius of a hydrogen nucleus, A = 1).
Nuclear volume V = (4/3)πR³ = (4/3)πR₀³ A, so V is proportional to the mass of the nucleus m = Au, where u is the atomic mass unit.
Nuclear density is given by ρ = 3u / (4πR₀³); since A cancels, density is the same for all nuclei and independent of radius.
Nuclear density is of the order 10¹⁷ kg m⁻³, significantly larger than atomic density, showing the nucleus contains most of the atom's mass and the atom is predominantly empty space.
In the Rutherford scattering experiment, α particles are fired at a thin gold foil; some come straight back due to electrostatic repulsion between the α particle and the gold nucleus.
At the point of closest approach d, the α particle's initial kinetic energy equals the electric potential energy: Ek = Ep = kQq/d = k(2e)(Ze)/d.
Rearranging gives d = k(2Ze²)/Ek, which gives a value for the radius of the nucleus (assuming high-energy α particles).
The charge of an α particle is 2e (2 protons); the charge of a target nucleus is Ze, where Z is the proton number.

Deviations from Rutherford Scattering

Rutherford's model predicted that as the scattering angle increases, the number of α particles scattered at that angle decreases; this holds at low to moderately high energies.
At very high energies (>27.5 MeV), significant deviations occur: the number of back-scattered α particles sharply decreases to zero instead of following the predicted relationship.
Rutherford's original model assumed α particles interact only through electrostatic repulsion.
If α particle energy exceeds 27.5 MeV, they get close enough to interact with the nucleus via the strong nuclear force.
Factoring in the strong nuclear force explains the observed scattering pattern, so deviations provide evidence for the strong nuclear force.
Deviations are greatest when α particles have high energies and target nuclei have low nucleon number (e.g., aluminium vs gold).
At very small separations (<1.5 fm), the strong nuclear force becomes significant.

Rutherford's Alpha Scattering Experiment

The Bohr Model of Hydrogen

Hydrogen is the simplest atom, ideal for investigating electron energy levels; its line spectra show electrons transition between specific energy levels, producing photons of specific energies.
Transitions are grouped into series: Lyman series converges on n = 1 (ultraviolet, highest energy photons); Balmer series converges on n = 2; Ritz-Paschen on n = 3; Pfund series converges on n = 5 (infrared, lowest energy photons).
The Bohr model states that electrons can only move in fixed orbits and the orbital radius is restricted to certain values.
The discrete energy levels of hydrogen are given by E = −13.6/n² eV, where n is an integer (1, 2, 3, ...).
Angular momentum is quantised: L = n(h/2π), where n is an integer, h is Planck's constant; angular momentum for an electron in a circular orbit is constant.
de Broglie proposed that an electron with momentum p = mv has a wavelength λ = h/p; for a circular orbit, the matter wave must form a standing wave with constructive interference.
The condition for a standing wave is nλ = 2πr, leading to the Bohr condition: nh/2π = mvr.
A limitation of the Bohr model is that it cannot explain the spectra of atoms with more than one electron.

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练习题

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1.Which of the following is the correct definition of an isotope?
Easy
- AAtoms of the same element with the same number of protons but different numbers of neutrons
- BAtoms of different elements with the same nucleon number
- CAtoms of the same element with the same number of neutrons but different numbers of protons
- DAtoms that have lost or gained electrons to become charged
2.In the notation for a nuclide, what does the top number A represent?
Easy
- AThe total number of protons and neutrons in the nucleus
- BThe total number of protons in the nucleus
- CThe total number of neutrons in the nucleus
- DThe total number of electrons in the atom
3.Which subatomic particle has a relative charge of +1 and a mass of approximately 1 u?
Easy
- AProton
- BNeutron
- CElectron
- Dα particle
4.In Rutherford's gold foil experiment, what observation led him to conclude that the atom is mostly empty space?
Medium
- AMost α particles passed straight through the foil undeflected.
- BA small number of α particles were deflected through angles greater than 90°.
- CSome α particles were deflected through small angles of less than 10°.
- Dα particles were absorbed by the gold foil.
5.Which statement about nuclear density is correct?
Medium
- AIt is the same for all nuclei and independent of the nuclear radius.
- BIt increases as the nucleon number increases.
- CIt decreases as the nucleon number increases.
- DIt is proportional to the volume of the nucleus.
6.An emission spectrum consists of:
Medium
- ABright coloured lines on a dark background
- BDark lines on a continuous coloured background
- CA continuous spectrum of all wavelengths
- DA single bright line
7.Which of the following gives the energy of a photon in terms of its wavelength λ?
Medium
- AE = hc/λ
- BE = hλ/c
- CE = hf
- DE = λ/hc
8.In the Bohr model of the hydrogen atom, the energy of an electron in level n is given by E = −13.6/n² eV. What is the energy of the electron in the ground state?
Medium
- A−13.6 eV
- B−3.4 eV
- C−1.51 eV
- D0 eV

更多题目

9.Which of the following is a limitation of the Bohr model of the hydrogen atom?
Hard
- AIt cannot explain the spectra of atoms with more than one electron.
- BIt predicts that electrons can exist at any radius.
- CIt does not include the concept of energy levels.
- DIt cannot explain the emission spectrum of hydrogen.
10.Which of the following statements about the Rutherford scattering experiment are correct? (Select all that apply)
Medium
- AThe experiment was conducted in an evacuated chamber to prevent α particles from colliding with air molecules.
- BA thin gold foil was used because a thicker foil would stop the α particles completely.
- CThe lead container was used to produce a collimated beam of α particles.
- DThe majority of α particles were deflected through angles greater than 90°.
- EThe experiment provided evidence for the existence of the neutron.
11.Which of the following are properties of photons? (Select all that apply)
Medium
- AThey are massless packets of electromagnetic energy.
- BThey travel at the speed of light in a vacuum.
- CThey have a negative charge.
- DTheir energy is directly proportional to their frequency.
- EThey can be split into smaller particles.
12.Isotopes of an element have the same number of protons but different numbers of neutrons.
Easy
True or false?
13.In an absorption spectrum, dark lines are observed on a continuous coloured background.
Easy
True or false?
14.The nuclear radius is directly proportional to the nucleon number A.
Medium
True or false?
15.Deviations from Rutherford scattering at very high energies provide evidence for the strong nuclear force.
Medium
True or false?
16.Match each term with its correct definition.
Medium
- Ionisation
- Photon
- Nuclide
- Isotope
- The process of removing an electron from an atom
- A massless packet of electromagnetic energy
- A species of atom with a specific proton and nucleon number
- Atoms of the same element with different numbers of neutrons
17.Place the following steps of the Rutherford scattering experiment in the correct chronological order.
Medium
- α particles are emitted from a source in a lead container.
- A collimated beam of α particles is directed at a thin gold foil.
- α particles interact with gold nuclei and are deflected.
- A movable detector measures the number and angles of deflected particles.
18.Match each subatomic particle with its correct relative charge and mass.
Medium
- Proton
- Neutron
- Electron
- +1 charge, ~1 u mass
- 0 charge, ~1 u mass
- -1 charge, ~0 u mass
19.Place the following steps to produce an emission spectrum in the correct chronological order.
Medium
- Electrons are excited to higher energy levels by heating.
- Electrons transition back to lower energy levels.
- Photons are emitted with specific wavelengths.
- A set of discrete coloured lines is observed on a black background.
20.In the Bohr model of the hydrogen atom, the energy of an electron in level n is given by E = -13.6/n² eV. What is the energy of the electron in the ground state (n = 1)?
Medium
- A-13.6 eV
- B13.6 eV
- C-3.4 eV
- D-1.51 eV
21.In a Rutherford scattering experiment, a student measures the number of α particles, n, detected per unit time at various angles θ from 0° to 90°. Which graph best represents how n varies with θ?
Medium
- An decreases rapidly as θ increases from 0°
- Bn increases rapidly as θ increases from 0°
- Cn remains constant for all θ
- Dn increases to a maximum at 45° then decreases
22.In a helium-neon laser, an electron in a helium atom is excited from the 1s ground state to the 2s level by collision with a free electron that initially has 45.0 eV of kinetic energy. The energy gap between 1s and 2s in helium is 21.2 eV. What is the kinetic energy of the free electron after the collision?
Hard
- A23.8 eV
- B21.2 eV
- C45.0 eV
- D66.2 eV
23.An α particle is fired head-on at a stationary gold nucleus (Z = 79). The distance of closest approach is d. If the α particle is replaced by a proton with the same initial kinetic energy, what is the new distance of closest approach?
Hard
- Ad/2
- Bd
- C2d
- D4d
24.In a Rutherford scattering experiment, α particles are fired at a thin gold foil. At very high energies above 27.5 MeV, the number of α particles back-scattered sharply decreases to zero instead of following the predicted electrostatic repulsion curve. What does this deviation provide evidence for?
Hard
- AThe strong nuclear force
- BThe electromagnetic force only
- CThe weak nuclear force
- DThe gravitational force
25.The density of a nucleus is given by ρ = 3u / (4πR₀³), where u is the atomic mass unit and R₀ = 1.20 × 10⁻¹⁵ m. What is the approximate value of nuclear density?
Medium
- A2.3 × 10¹⁷ kg m⁻³
- B2.3 × 10¹⁴ kg m⁻³
- C1.2 × 10¹⁵ kg m⁻³
- D9.2 × 10¹⁶ kg m⁻³
26.A fluorescent tube contains mercury vapour. An electron in a mercury atom is excited to level n = 4 and then de-excites to the ground state n = 1. Which of the following statements are correct? (Select all that apply)
Hard
- AThe photon with the lowest frequency is emitted by the transition with the smallest energy difference.
- BThe photon with the highest frequency is emitted by the transition with the largest energy difference.
- CThe number of possible different photon wavelengths emitted is 6.
- DAll transitions emit photons of the same wavelength.
- EThe transition from n = 4 to n = 1 emits the longest wavelength photon.
27.In a Rutherford scattering experiment, using a vacuum chamber is necessary because α particles are highly ionising and would collide with air molecules otherwise.
Medium
True or false?
28.The density of a nucleus changes significantly after it undergoes radioactive decay.
Medium
True or false?
29.Match each spectral series of hydrogen with the energy level it converges on.
Medium
- Lyman series
- Balmer series
- Ritz-Paschen series
- n = 1
- n = 2
- n = 3
30.Place the following steps in the correct order to describe how an emission spectrum is produced.
Medium
- Energy is supplied to a low-pressure gas, exciting electrons to higher energy levels.
- Electrons transition back down to lower energy levels.
- Photons of specific wavelengths are emitted.
- A set of discrete coloured lines is observed on a black background.
31.In a Rutherford scattering experiment, α particles are fired at a thin aluminium foil (Z = 13) instead of gold (Z = 79). The foils have the same thickness. Compared to gold, what is the predicted difference in the scattering pattern?
Challenge
- AMore deviation from Rutherford scattering is seen with aluminium because α particles can get closer to the lower-charge nucleus and interact via the strong nuclear force.
- BLess deviation is seen with aluminium because the lower charge means weaker electrostatic repulsion.
- CThe same deviation is seen because the scattering pattern depends only on the α particle energy.
- DMore deviation is seen with gold because its higher charge causes stronger repulsion.
32.The radius of an electron's orbit in a singly ionised helium atom (one electron removed) is 2.43 × 10⁻¹⁰ m. Using the Bohr model, what is the principal quantum number of the energy level occupied by the electron? (Use r = n² × 0.529 × 10⁻¹⁰ / Z, where Z = 2 for helium.)
Hard
- An = 3
- Bn = 2
- Cn = 4
- Dn = 1
33.In the Rutherford scattering experiment, why is the α particle source placed inside a lead container with a narrow hole?
Medium
- ATo produce a collimated beam of α particles, since lead absorbs them
- BTo slow down the α particles before they reach the foil
- CTo shield the detector from gamma radiation emitted by the foil
- DTo ionise the air inside the chamber so the particles can travel further
34.Why must the gold foil used in Rutherford's scattering experiment be extremely thin, about 10^-6 m thick?
Medium
- ASo that α particles are not all stopped by the foil, allowing some to pass through
- BSo that the gold atoms are ionised and emit a spectrum
- CSo that the α particles are deflected by the strong nuclear force
- DSo that the foil does not melt under the intense α beam
35.Why is the α particle scattering experiment carried out inside an evacuated chamber?
Medium
- ASo that the α particles do not collide with air molecules before reaching the foil
- BSo that the gold foil does not oxidise in air
- CTo increase the kinetic energy of the α particles
- DTo prevent the detector from overheating
36.In a Rutherford scattering experiment, the number of α particles n detected per unit time at deflection angle θ drops rapidly as θ increases from 0° to 90°. Which graph best represents this variation?
Medium
- AA curve that starts high at θ = 0° and falls steeply towards zero as θ increases
- BA straight line rising from zero at θ = 0° to a maximum at θ = 90°
- CA horizontal line at constant n for all θ
- DA curve that starts low at θ = 0° and rises to a peak at θ = 90°
37.Which of the following statements about deviations from Rutherford scattering are correct? (Select all that apply)
Hard
- ASignificant deviations occur when α particle energies exceed about 27.5 MeV
- BThe deviations provide evidence for the strong nuclear force
- Cα particles get close enough to interact with nucleons via the strong nuclear force at very small separations
- DDeviations occur because the α particles are attracted to the nucleus by the electric force
- EThe number of back-scattered α particles increases sharply at very high energies
38.In a Rutherford scattering experiment, α particles are fired at a thin aluminium foil (Z = 13) instead of gold (Z = 79), the foils having the same thickness. Compared with gold, which change in the scattering pattern is predicted?
Hard
- AMore deviation from Rutherford scattering, because α particles get closer to the less charged aluminium nuclei
- BLess deviation, because aluminium nuclei exert a stronger electric repulsion
- CNo change, because the scattering pattern depends only on the α particle energy
- DMore back-scattering at large angles, because aluminium has a smaller nucleon number
39.In the Bohr model, which condition must be satisfied for a stable electron orbit to exist?
Medium
- AThe circumference of the orbit must equal an integer number of de Broglie wavelengths
- BThe kinetic energy of the electron must equal its potential energy
- CThe electron must be at rest at the centre of the nucleus
- DThe angular momentum of the electron must be zero
40.In the Rutherford scattering experiment, the majority of α particles pass straight through the gold foil undeflected.
Easy
True or false?
41.Calculate the wavelength of a photon with an energy of 1.44 × 10⁻¹⁹ J. Give your answer in nm.
Medium
42.Calculate the nuclear radius of carbon-14 (¹⁴C) using R = R₀A^(1/3) with R₀ = 1.20 × 10⁻¹⁵ m. Give your answer in fm (femtometres).
Medium
43.Complete the definitions by filling in the blanks.
Easy
Ionisation is the process of removing an ____ from an atom. A ____ is a massless packet of electromagnetic energy. A ____ is a species of atom characterised by a specific proton number and nucleon number.
44.In the equation E = hc/λ, identify the meaning and unit of each symbol.
Medium
h is ____ with unit ____. c is ____ with unit ____. λ is ____ with unit ____.
45.What term describes an atom that has lost or gained electrons?
Easy
46.What is the name of the series of spectral lines in the hydrogen spectrum that converges on the ground state (n = 1)?
Easy
47.Calculate the wavelength of a photon with an energy of 1.44 × 10^-19 J. Give your answer in nm.
Medium
48.A helium-neon laser produces photons of wavelength 632.8 nm. Calculate the energy of one photon in eV. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, and 1 eV = 1.60 × 10⁻¹⁹ J. Give your answer to 2 significant figures.
Hard
49.An α particle with an initial speed of 3.00 × 10⁷ m s⁻¹ is fired head-on at a stationary gold nucleus (Z = 79). Calculate the minimum separation between the α particle and the centre of the gold nucleus, in femtometres (fm). Use k = 8.99 × 10⁹ N m² C⁻², e = 1.60 × 10⁻¹⁹ C, and mass of α particle = 6.64 × 10⁻²⁷ kg. Give your answer to 2 significant figures.
Hard
50.Complete the following statements about the Bohr model of hydrogen by filling in the blanks.
Medium
The Lyman series converges on the energy level n = ____ and produces photons mainly in the ____ region of the electromagnetic spectrum. The Balmer series converges on n = ____ and produces photons mainly in the visible region.
51.In a helium-neon laser, a helium atom is excited and then collides with a ground-state neon atom, transferring energy. The neon atom becomes excited and emits two photons to return to its ground state. If one photon has an energy of 1.96 eV and the total energy transferred to the neon atom is 3.50 eV, calculate the wavelength of the other photon in nm. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, and 1 eV = 1.60 × 10⁻¹⁹ J. Give your answer to 3 significant figures.
Hard
52.Complete the following statements about the Rutherford scattering experiment by filling in the blanks.
Medium
The α particle source is placed in a ____ container to produce a collimated beam. The gold foil is extremely thin, about ____ m thick, because a thicker foil would stop the α particles completely. The apparatus is placed in an ____ chamber to prevent α particles from colliding with air molecules.
53.Explain how atomic spectra provide evidence for the quantisation of energy in atoms.
Hard
54.Outline how the density of a nucleus varies with nuclear radius.
Medium
55.Explain why it is not possible for a free electron with 45.0 eV of kinetic energy to collide with a ground-state helium atom (1s to 2s energy gap = 21.2 eV) and be left with 40.0 eV of kinetic energy.
Hard
56.Explain why Rutherford's model of the atom can account for both small-angle and large-angle deflections of α particles, whereas Thomson's model cannot account for large-angle deflections.
Hard
57.Explain why it is not possible for the same electron to collide with a ground-state helium atom and be left with 40.0 eV of kinetic energy, given that the 1s to 2s energy gap is 21.2 eV.
Hard
58.Calculate the wavelength of a photon with an energy of 1.44 × 10⁻¹⁹ J. Give your answer in nm.
Medium
- A1518 nm
- B1656 nm
- C1380 nm
- D1242 nm
59.Calculate the nuclear radius of carbon-14 (¹⁴C) using R = R₀A^(1/3) with R₀ = 1.20 × 10⁻¹⁵ m. Give your answer in fm (femtometres).
Medium
- A3.9 fm
- B4.9 fm
- C2.9 fm
- D1.9 fm
60.Calculate the wavelength of a photon with an energy of 1.44 × 10^-19 J. Give your answer in nm.
Medium
- A1380 nm
- B1518 nm
- C1656 nm
- D1242 nm
61.A helium-neon laser produces photons of wavelength 632.8 nm. Calculate the energy of one photon in eV. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, and 1 eV = 1.60 × 10⁻¹⁹ J. Give your answer to 2 significant figures.
Hard
- A2.96 eV
- B1.96 eV
- C3.96 eV
- D0.96 eV
62.An α particle with an initial speed of 3.00 × 10⁷ m s⁻¹ is fired head-on at a stationary gold nucleus (Z = 79). Calculate the minimum separation between the α particle and the centre of the gold nucleus, in femtometres (fm). Use k = 8.99 × 10⁹ N m² C⁻², e = 1.60 × 10⁻¹⁹ C, and mass of α particle = 6.64 × 10⁻²⁷ kg. Give your answer to 2 significant figures.
Hard
- A44 fm
- B40 fm
- C36 fm
- D32 fm
63.In a helium-neon laser, a helium atom is excited and then collides with a ground-state neon atom, transferring energy. The neon atom becomes excited and emits two photons to return to its ground state. If one photon has an energy of 1.96 eV and the total energy transferred to the neon atom is 3.50 eV, calculate the wavelength of the other photon in nm. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, and 1 eV = 1.60 × 10⁻¹⁹ J. Give your answer to 3 significant figures.
Hard
- A875 nm
- B656 nm
- C807 nm
- D729 nm

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