p.16
Atomic Spectra and Emission Lines
What occurs when an atom absorbs a photon with precise energy?
It can transition to a higher energy state.
p.16
Rydberg Formula and Spectral Series
What is the Rydberg formula used for?
To describe the spectrum of the hydrogen atom.
p.18
De Broglie's Wave-Particle Duality
What did Louis de Broglie argue about the electron in its circular orbit?
The electron must be seen as a particle wave.
p.1
J.J. Thomson's Plum Pudding Model
What did J. J. Thomson discover in 1897?
That atoms contain negatively charged constituents (electrons) that are identical for all atoms.
p.1
J.J. Thomson's Plum Pudding Model
Why are atoms electrically neutral?
Because they contain both negatively charged electrons and some positive charge to neutralize them.
p.8
Rydberg Formula and Spectral Series
What is a spectral series?
Sets of spectral lines that exhibit a regular pattern.
p.7
Bohr Model of the Hydrogen Atom
What does the negative sign in the electrostatic potential energy (U) signify?
It signifies that the electrostatic force is in the –r direction.
p.10
Rutherford's Nuclear Model of the Atom
What contradiction arises from the classical electromagnetic theory regarding emitted light from electrons?
It predicts a continuous spectrum instead of the observed line spectrum.
p.10
Bohr Model of the Hydrogen Atom
Who is Niels Bohr and what did he contribute to atomic theory?
A Danish physicist who explained the spectrum of the hydrogen atom based on quantum ideas.
p.10
Bohr Model of the Hydrogen Atom
What principle did Niels Bohr propose to clarify conceptual problems in quantum mechanics?
The complementary principle.
p.19
Bohr Model of the Hydrogen Atom
What does the Bohr model primarily involve in its formulation?
The electrical force between the positively charged nucleus and the electron.
p.16
Rydberg Formula and Spectral Series
What are the names of the series identified for the hydrogen atom?
Lyman, Balmer, Paschen, Brackett, and Pfund series.
p.17
Atomic Spectra and Emission Lines
What do dark spectral absorption lines indicate when photons pass through a rarefied gas?
The frequencies that have been absorbed by the atoms of the gas.
p.2
Rutherford's Nuclear Model of the Atom
What is concentrated in the nucleus according to Rutherford's model?
The entire positive charge and most of the mass of the atom.
p.4
Alpha-Particle Scattering Experiment
What happens when an alpha-particle comes near a nucleus?
It is scattered through a large angle due to the intense electric field.
p.16
Quantization of Angular Momentum
What is indicated by the integers n_f and n_i in the Rydberg formula?
They represent different atomic energy levels.
p.1
Atomic Spectra and Emission Lines
What type of radiation do condensed matter and dense gases emit?
Electromagnetic radiation with a continuous distribution of several wavelengths.
p.17
Rydberg Formula and Spectral Series
What are the wavelengths of the first four lines in the Lyman series of the hydrogen spectrum?
1218 Å, 1028 Å, 974.3 Å, and 951.4 Å.
p.19
Applications of Laser Technology
What experiment did Apollo astronauts conduct with lasers on the moon?
They placed a mirror on the moon to reflect a laser beam back to Earth for distance measurement.
p.2
Rutherford's Nuclear Model of the Atom
What did Rutherford estimate regarding the atomic nucleus?
The approximate size of the nucleus.
p.9
Atomic Spectra and Emission Lines
What is the relationship between wavelength and frequency in the context of the Balmer formula?
c = νλ, where c is the speed of light.
p.9
Rutherford's Nuclear Model of the Atom
What does the Rutherford model of the atom assume?
The atom consists of a central nucleus and revolving electrons, similar to a sun-planet system.
p.11
Atomic Spectra and Emission Lines
What is the relationship between the frequency of the emitted photon and the energy states?
hν = Ei - Ef, where Ei and Ef are the energies of the initial and final states.
p.16
Atomic Spectra and Emission Lines
What happens when an electron transitions from a higher energy state to a lower energy state?
Photons are emitted, producing spectral lines.
p.1
Historical Development of Atomic Theory
What significant evidence accumulated by the nineteenth century regarding matter?
Evidence in favor of the atomic hypothesis.
p.13
Bohr Model of the Hydrogen Atom
What assumption is made in the derivation of Eqs. (12.17) – (12.19)?
That the electronic orbits are circular.
p.7
Bohr Model of the Hydrogen Atom
What are the expressions for kinetic energy (K) and electrostatic potential energy (U) of the electron in a hydrogen atom?
K = 2 2 0 1 mv^2 and U = -2 8 4 e^2/r.
p.2
Rutherford's Nuclear Model of the Atom
What did Rutherford's experiments with alpha-particles lead to?
The birth of Rutherford’s planetary model of the atom.
p.19
Bohr Model of the Hydrogen Atom
What aspect of hydrogen's emission spectrum does the Bohr model fail to explain?
The relative intensities of the frequencies.
p.18
Bohr Model of the Hydrogen Atom
What limitation does the Bohr model have regarding multi-electron atoms?
It cannot be extended to atoms with more than one electron, such as helium.
p.6
Alpha-Particle Scattering Experiment
What is the radius of the gold nucleus compared to the calculated distance of closest approach?
The radius of the gold nucleus is less than 3.0 × 10⁻¹⁴ m, while the actual radius is 6 fm.
p.9
Atomic Spectra and Emission Lines
What is the formula for the Lyman series?
R(1/n²) for n = 2, 3, 4...
p.5
Alpha-Particle Scattering Experiment
What is the formula for the force on an α-particle in relation to the nucleus?
F = (2)(Ze^2)/r^2, where r is the distance between the α-particle and the nucleus.
p.6
Rutherford's Nuclear Model of the Atom
What force keeps the electrons in their orbits according to the Rutherford model?
The electrostatic force of attraction between the electrons and the nucleus.
p.17
De Broglie's Wave-Particle Duality
What did C. J. Davisson and L. H. Germer experimentally verify?
The wave nature of electrons.
p.11
Quantization of Angular Momentum
What defines the stable orbits according to Bohr's second postulate?
The angular momentum is an integral multiple of h/2π.
p.10
Rutherford's Nuclear Model of the Atom
What happens to an accelerating charged particle according to classical electromagnetic theory?
It emits radiation in the form of electromagnetic waves.
p.20
Historical Development of Atomic Theory
What is the overall charge of an atom?
Electrically neutral, containing equal amounts of positive and negative charges.
p.4
Alpha-Particle Scattering Experiment
Why do most alpha-particles pass through a thin metal foil?
Because most of an atom is empty space.
p.7
Bohr Model of the Hydrogen Atom
What is the total energy (E) of the electron in a hydrogen atom?
E = K + U = -2 0 8 e^2/r.
p.13
Bohr Model of the Hydrogen Atom
How does quantum mechanics differ from the Bohr model in describing electron motion?
Quantum mechanics describes electron motion in terms of probabilities rather than definite paths.
p.19
Applications of Laser Technology
How does laser light differ from light emitted by ordinary sources?
Laser light has better phase correlation and a more uniform wavelength.
p.2
Alpha-Particle Scattering Experiment
Who performed the experiments suggested by Rutherford in 1911?
H. Geiger and E. Marsden.
p.12
Bohr Model of the Hydrogen Atom
What is the expression for the total energy of the electron in the hydrogen atom?
Eₙ = - (2.18 × 10⁻¹⁸ J)/n².
p.8
Rydberg Formula and Spectral Series
What happens to the spacing between lines in the hydrogen spectrum as the wavelength decreases?
The lines appear closer together and are weaker in intensity.
p.19
Applications of Laser Technology
What does the successful reflection of a laser beam from the moon allow scientists to measure?
The extremely small divergence of a laser beam and the distance of the moon from the Earth.
p.12
Bohr Model of the Hydrogen Atom
What does the negative sign in the total energy of an electron indicate?
The electron is bound to the nucleus.
p.20
Quantization of Angular Momentum
What is Bohr's quantization condition?
Angular momentum L = nh/2π, where n is an integer called a quantum number.
p.11
Bohr Model of the Hydrogen Atom
What was Bohr's first postulate about electrons in an atom?
An electron can revolve in certain stable orbits without emitting radiant energy.
p.5
Rutherford's Nuclear Model of the Atom
What does the comparison of atomic and solar system dimensions imply about atomic structure?
It implies that an atom contains a much greater fraction of empty space than our solar system does.
p.14
Atomic Spectra and Emission Lines
What is the relationship between the energy levels and the quantum number n in a hydrogen atom?
As n increases, the energy levels become less negative, indicating higher energy states.
p.8
Atomic Spectra and Emission Lines
What does the emission line spectrum of atomic hydrogen consist of?
Bright lines on a dark background.
p.8
Atomic Spectra and Emission Lines
What can the study of emission line spectra serve as for gases?
A type of 'fingerprint' for identification.
p.18
Quantization of Angular Momentum
What is the relationship between the circumference of the electron's orbit and its wavelength?
2 π r_n = n λ, where n = 1, 2, 3...
p.19
Bohr Model of the Hydrogen Atom
What limitation does the Bohr model have regarding multi-electron atoms?
It does not include the electrical forces between electrons.
p.16
Bohr Model of the Hydrogen Atom
What does the agreement between theoretical and experimental values of the Rydberg constant confirm?
It provides a direct confirmation of Bohr's model.
p.12
Bohr Model of the Hydrogen Atom
What is the formula for the size of the innermost orbit (n=1)?
r₁ = (2h²)/(me²), known as the Bohr radius (a₀).
p.4
Alpha-Particle Scattering Experiment
What is the charge of an alpha-particle?
2 e (two units of positive charge).
p.4
Alpha-Particle Scattering Experiment
What laws are used to compute the trajectory of an alpha-particle during scattering?
Newton’s second law of motion and Coulomb’s law for electrostatic force of repulsion.
p.7
Atomic Spectra and Emission Lines
What type of spectrum does an atomic gas or vapor emit when excited?
An emission line spectrum.
p.12
Bohr Model of the Hydrogen Atom
What energy is required to remove the electron from the hydrogen atom?
Energy is required to move the electron to a distance infinitely far from the nucleus.
p.11
Atomic Spectra and Emission Lines
What does Bohr's third postulate state about electron transitions?
An electron can transition between non-radiating orbits, emitting a photon with energy equal to the energy difference.
p.3
Alpha-Particle Scattering Experiment
How were the α-particles collimated before hitting the gold foil?
By passing through lead bricks.
p.10
Rutherford's Nuclear Model of the Atom
What would happen to an electron in an atom according to classical electromagnetic theory?
It would spiral inward and eventually fall into the nucleus.
p.4
Rutherford's Nuclear Model of the Atom
What did Rutherford's experiments suggest about the structure of the atom?
The entire positive charge and most of the mass are concentrated in the nucleus, with electrons orbiting at a distance.
p.7
Bohr Model of the Hydrogen Atom
What is the relation between the orbit radius and the electron velocity in a hydrogen atom?
The relation is given by the equation 2 2 0 4 e r mv.
p.2
Rydberg Formula and Spectral Series
What did Johann Jakob Balmer establish in 1885?
A simple empirical formula for the wavelengths of lines emitted by atomic hydrogen.
p.18
De Broglie's Wave-Particle Duality
What is the de Broglie wavelength of an electron moving in the n-th orbit?
λ = h/p, where p is the electron's momentum.
p.1
J.J. Thomson's Plum Pudding Model
How did Thomson describe the arrangement of charges in his model?
The positive charge is uniformly distributed throughout the atom, with electrons embedded like seeds in a watermelon.
p.19
Applications of Laser Technology
What is the acronym LASER stand for?
Light Amplification by Stimulated Emission of Radiation.
p.2
Rutherford's Nuclear Model of the Atom
What was a major limitation of Rutherford's nuclear model?
It could not explain why atoms emit light of only discrete wavelengths.
p.18
Bohr Model of the Hydrogen Atom
What are hydrogenic atoms?
Atoms consisting of a nucleus with positive charge +Ze and a single electron.
p.20
Rutherford's Nuclear Model of the Atom
What are the two main difficulties of Rutherford's nuclear model?
(a) It predicts atoms are unstable due to spiraling electrons, contradicting matter's stability. (b) It cannot explain the characteristic line spectra of different elements.
p.13
Bohr Model of the Hydrogen Atom
For which type of atoms is the Bohr model valid?
Only one-electron atoms/ions.
p.4
Rutherford's Nuclear Model of the Atom
How does the mass of the gold nucleus compare to that of an alpha-particle?
The gold nucleus is about 50 times heavier than an alpha-particle.
p.6
Rutherford's Nuclear Model of the Atom
What does the Rutherford nuclear model depict?
An atom as a positively charged nucleus surrounded by revolving electrons in stable orbits.
p.13
Quantization of Angular Momentum
What is the relationship between energy and the principal quantum number n in the Bohr model?
Energy depends only on the principal quantum number n for one-electron atoms/ions.
p.9
Atomic Spectra and Emission Lines
Which elements have spectra that can be represented by simple formulas?
Hydrogen, singly ionized helium, and doubly ionized lithium.
p.5
Alpha-Particle Scattering Experiment
What happens to an α-particle in a head-on collision with the nucleus?
The α-particle rebounds back with an angle θ ≈ π.
p.3
Alpha-Particle Scattering Experiment
What type of particles were directed at the gold foil in the Geiger-Marsden experiment?
5.5 MeV α-particles emitted from a 21483 Bi radioactive source.
p.3
Alpha-Particle Scattering Experiment
What does the solid curve in the experiment's graph represent?
The theoretical prediction based on the assumption of a small, dense, positively charged nucleus.
p.14
Atomic Spectra and Emission Lines
What is the significance of the energy level diagram for a hydrogen atom?
It shows the allowed energy states and the energy required for transitions between them.
p.2
Rutherford's Nuclear Model of the Atom
What governs the interactions of atoms and molecules?
The interaction of each atom or molecule with its neighbors.
p.2
Atomic Spectra and Emission Lines
What is observed in the spectrum of light emitted from rarefied gases?
A series of bright lines at discrete wavelengths.
p.13
Bohr Model of the Hydrogen Atom
Who showed that the equations hold for elliptical orbits as well?
German physicist Arnold Sommerfeld.
p.4
Rutherford's Nuclear Model of the Atom
How much larger is the size of an atom compared to its nucleus?
About 10,000 to 100,000 times larger.
p.6
Alpha-Particle Scattering Experiment
What principle is used to determine the distance of closest approach in the Geiger-Marsden experiment?
The conservation of total mechanical energy of the system.
p.13
Quantization of Angular Momentum
What does the quantization of angular momentum refer to in the Bohr model?
Electrons moving in definite orbits have quantized angular momentum.
p.20
J.J. Thomson's Plum Pudding Model
How does Thomson's model describe the atom?
As a spherical cloud of positive charges with electrons embedded in it.
p.9
Atomic Spectra and Emission Lines
What happens beyond the limit of the Balmer series?
Only a faint continuous spectrum is seen.
p.7
Bohr Model of the Hydrogen Atom
What does a negative total energy (E) imply about the electron in a hydrogen atom?
It implies that the electron is bound to the nucleus.
p.20
Atomic Spectra and Emission Lines
What does the line spectrum of an atom consist of?
A set of isolated parallel lines termed as line spectrum, providing information about atomic structure.
p.13
Atomic Spectra and Emission Lines
What does the wave function obtained from the Schrödinger equation provide?
Information about the probability of finding an electron in various regions around the nucleus.
p.20
Bohr Model of the Hydrogen Atom
What are the three postulates of Bohr's model for hydrogenic atoms?
(a) Electrons revolve in stable orbits without emitting energy. (b) Angular momentum is an integral multiple of h/2π. (c) Electrons can transition between orbits, emitting or absorbing photons.
p.5
Alpha-Particle Scattering Experiment
How does the impact parameter affect the trajectory of an α-particle?
A small impact parameter results in large scattering, while a large impact parameter leads to nearly undeviated paths.
p.5
Alpha-Particle Scattering Experiment
What does the small fraction of α-particles that rebound back indicate about the atom?
It indicates that the mass of the atom is concentrated in a small volume.
p.18
De Broglie's Wave-Particle Duality
What condition leads to the formation of standing waves in a string?
The total distance travelled by a wave must be an integral number of wavelengths.
p.4
Rutherford's Nuclear Model of the Atom
What is the estimated size of the nucleus according to Rutherford's model?
About 10^-15 m to 10^-14 m.
p.13
Bohr Model of the Hydrogen Atom
What revolutionary idea did Bohr introduce regarding electron orbits?
Definite energy orbits for electrons.
p.12
Bohr Model of the Hydrogen Atom
What does Eq. (12.14) depict about orbital speed?
The orbital speed in the n-th orbit falls by a factor of n.
p.17
Bohr Model of the Hydrogen Atom
What significant achievement did Bohr accomplish regarding the hydrogen atom spectrum?
He provided an explanation that greatly stimulated progress towards modern quantum theory.
p.6
Alpha-Particle Scattering Experiment
What is the initial mechanical energy of the α-particle before interaction?
The kinetic energy K of the incoming α-particle.
p.1
J.J. Thomson's Plum Pudding Model
What did subsequent studies reveal about Thomson's model?
The distribution of electrons and positive charges is very different from that proposed in the Plum Pudding Model.
p.6
Alpha-Particle Scattering Experiment
What does the final energy of the α-particle represent when it momentarily stops?
The electric potential energy U of the system.
p.9
Atomic Spectra and Emission Lines
What are the names of the other series of spectra for hydrogen?
Lyman, Paschen, Brackett, and Pfund series.
p.12
Bohr Model of the Hydrogen Atom
How do the radii of the orbits change with respect to n?
The radii of the orbits increase as n².
p.18
Bohr Model of the Hydrogen Atom
What does the Bohr model correctly predict?
The gross features of hydrogenic atoms, particularly the frequencies of emitted or absorbed radiation.
p.20
Rydberg Formula and Spectral Series
What is the significance of the Lyman, Balmer, and Paschen series?
They represent different series of line spectra emitted by atomic hydrogen.
p.13
Bohr Model of the Hydrogen Atom
What is the significance of the example involving a satellite in the context of Bohr's angular momentum postulate?
It applies Bohr's angular momentum postulate to a macroscopic object, suggesting a quantum number for the satellite's orbit.
p.20
Atomic Spectra and Emission Lines
How is the frequency of an emitted photon related to energy levels?
The frequency (ν) is given by hν = Ei - Ef, where Ei and Ef are the initial and final energy states.
p.5
Rutherford's Nuclear Model of the Atom
In the analogy of the Rutherford model, how does the size of the electron's orbit compare to the nucleus?
The radius of the electron's orbit is 10^5 times larger than the radius of the nucleus.
p.11
Quantization of Angular Momentum
What is the significance of the quantization condition in Bohr's model?
It determines the allowed values of angular momentum for electrons in orbits.
p.14
Atomic Spectra and Emission Lines
What happens to a hydrogen atom when it receives sufficient energy?
It may raise the electron to higher energy states, becoming an excited state.
p.18
Quantization of Angular Momentum
What does the de Broglie hypothesis explain in relation to Bohr's model?
It provides an explanation for the quantization of angular momentum of the orbiting electron.
p.20
Rutherford's Nuclear Model of the Atom
What is the main feature of Rutherford's model of the atom?
Most of the mass and all positive charge are concentrated in a tiny nucleus, with electrons revolving around it.
p.17
Rydberg Formula and Spectral Series
What is the Rydberg formula used for?
To calculate the wavelengths of spectral lines in the hydrogen spectrum.
p.19
Applications of Laser Technology
What is the relationship between the number of atoms and intensity in ordinary light sources versus laser sources?
In ordinary sources, intensity is proportional to NI; in laser sources, it is proportional to N²I.
p.17
Quantization of Angular Momentum
What does Bohr's second postulate state about the angular momentum of an electron?
It is quantized, given by L = nh/2π.
p.7
Bohr Model of the Hydrogen Atom
What is the velocity of the revolving electron in a hydrogen atom?
Approximately 2.2 × 10^6 m/s.
p.5
Alpha-Particle Scattering Experiment
What does the impact parameter 'b' represent in the context of α-particle collisions?
The perpendicular distance of the initial velocity vector of the α-particle from the center of the nucleus.
p.9
Rutherford's Nuclear Model of the Atom
What force holds the planetary system together, and how does it differ from the nucleus-electron system?
The planetary system is held by gravitational force, while the nucleus-electron system interacts by Coulomb’s Law of force.
p.5
Rutherford's Nuclear Model of the Atom
If the dimensions of the solar system were scaled to the proportions of an atom, how would the Earth's distance from the Sun change?
The Earth would be much farther away from the Sun than it actually is.
p.11
Bohr Model of the Hydrogen Atom
How is the radius of the electron orbit calculated in Bohr's model?
Using the quantization condition of angular momentum.
p.3
Alpha-Particle Scattering Experiment
What device was used to observe the scattered α-particles?
A rotatable detector consisting of a zinc sulphide screen and a microscope.
p.3
Alpha-Particle Scattering Experiment
What phenomenon occurs when α-particles strike the zinc sulphide screen?
They produce brief light flashes or scintillations.
