Chapter 32: The Atom And The Quantum

Electrons exhibit both wave and particle properties. This is known as the wave-particle duality of electrons. On one hand, electrons can behave as particles, as they have mass and charge, and can be localized at a specific position. On the other hand, they also exhibit wave-like characteristics, such as interference and diffraction, similar to light waves. This dual behavior is a fundamental concept in quantum mechanics and is supported by various experiments, such as the double-slit experiment. Therefore, the correct answer is that a beam of electrons has both wave and particle properties.

When Rutherford conducted his famous gold foil experiment, he observed that most of the alpha particles went almost straight through the foil. This result was unexpected as per the prevailing model of the atom at that time, which suggested that the positive charge in an atom is evenly distributed. Rutherford's observation led to the conclusion that the positive charge in an atom is concentrated in a small, dense nucleus, which explains why most of the alpha particles passed through the foil without significant deflection.

In the Bohr model of hydrogen, the electron is considered to have wave-like properties. According to de Broglie's theory, particles like electrons also exhibit wave-like behavior. The de Broglie wavelength is given by the equation λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. Since the electron's momentum is quantized in the Bohr model, the de Broglie wavelength will also be quantized. Therefore, the electron can only exist in certain energy states and orbit at specific radii, resulting in discrete radii and energy states in the Bohr model.

The Bohr model of the atom is considered defective and oversimplified because it does not fully explain the behavior of electrons in atoms. However, it is still useful in understanding the basic structure of atoms and for teaching introductory concepts in atomic theory. It provides a simplified framework for visualizing electron energy levels and the emission and absorption of photons. While more accurate models have been developed, the Bohr model remains a valuable tool for learning the fundamentals of atomic structure.

The correspondence principle states that a new theory must agree with the results of previous well-established theories in the appropriate limit. Therefore, it applies to all good theories, whether they describe submicroscopic or macroscopic phenomena. This principle ensures that new theories are consistent with the known laws of nature and helps to bridge the gap between different scales of observation.

The correct answer is that atoms of gold, like any others, are mostly empty space. This is because atoms are made up of a nucleus, which contains protons and neutrons, surrounded by electrons. The nucleus is very small compared to the overall size of the atom, and the electrons are located in energy levels or orbitals that are spread out around the nucleus. This means that most of the space within an atom is empty, with only a small portion occupied by the nucleus and electrons. Therefore, when alpha particles are fired at a gold foil, they are able to pass through undeflected because they mostly encounter empty space within the gold atoms.

Niels Bohr's explanation suggests that an electron in an excited state can emit several photons in a series of transitions to the ground state. This means that when an electron moves from a higher energy level to a lower energy level, it releases energy in the form of multiple photons. This concept aligns with Bohr's atomic model, which states that electrons exist in specific energy levels and can transition between them by absorbing or emitting photons. Therefore, the correct answer is that an electron in an excited state can give off several photons in a series of transitions to the ground state.

The Bohr model of the atom is often compared to a miniature solar system because it depicts the electrons orbiting around the nucleus in specific energy levels, similar to how planets orbit the sun. This analogy helps to visualize the structure of the atom and understand the concept of electron energy levels.

Electrons and protons both have charge. Charge is a fundamental property of subatomic particles, and it can be positive or negative. Electrons have a negative charge, while protons have a positive charge. The magnitude of the charge of an electron is equal to the magnitude of the charge of a proton. Therefore, the correct answer is "charge."

The quantization of electron energy states in an atom is better understood in terms of the electron's wave nature. This is because the wave nature of electrons allows them to exist in discrete energy levels or orbitals around the nucleus. The concept of wave-particle duality suggests that electrons can exhibit both wave-like and particle-like properties, but when it comes to understanding the energy states in an atom, the wave nature is more relevant. The wave nature of electrons helps explain phenomena such as electron diffraction and the wavefunction, which describes the probability distribution of finding an electron in a particular energy state.

The quantum-mechanical probability cloud for the electron in the hydrogen atom refers to the region where the electron is most likely to be found. The average radius of this cloud is said to agree with the orbital radius of Bohr, which means that the average distance of the electron from the nucleus matches the predicted radius by Bohr's model of the atom. This suggests that the quantum-mechanical model supports and aligns with Bohr's orbital theory in terms of the electron's location within the hydrogen atom.

The explanation for the correct answer is that both energy conservation and the physicist W. Ritz support the statement. Energy conservation states that the total energy before and after a process remains constant, so the sum of the frequencies of the two photons emitted during the de-excitation process must equal the frequency of the single photon emitted during direct de-excitation. W. Ritz, a physicist, developed the Ritz combination principle, which states that the frequency of a photon emitted during a transition between two energy levels is equal to the sum or difference of the frequencies of two photons emitted during a series of transitions between the same energy levels. Therefore, both energy conservation and W. Ritz support the given statement.

The correct answer is the wave nature of the electron. According to quantum mechanics, electrons exhibit wave-particle duality, meaning they can behave as both particles and waves. The wave nature of electrons allows them to exist in a stable orbital around the nucleus without losing energy and spiraling into it. This is because the electron's wave function spreads out in space, creating a standing wave pattern that is stable and does not collapse into the nucleus. Therefore, the wave nature of the electron prevents it from spiraling into the nucleus.

The average diameter of a helium atom is smaller compared to the average diameter of a hydrogen atom. This is because helium has a higher atomic number and more protons and neutrons in its nucleus, which results in a stronger attractive force between the electrons and the nucleus. As a result, the electrons are pulled closer to the nucleus, leading to a smaller atomic size. On the other hand, hydrogen has only one proton in its nucleus, resulting in a larger atomic size.

When an excited hydrogen atom returns to its ground state, it releases energy in the form of electromagnetic radiation. This radiation can have different wavelengths, corresponding to different frequencies. Since the electron in the atom can transition to different energy levels, it can emit radiation at multiple frequencies. Therefore, an excited hydrogen atom is capable of emitting radiation of many more than 3 frequencies.

The key feature of the theory of chaos is that very small initial differences can lead to very large eventual differences. This means that even a tiny change in the starting conditions of a chaotic system can result in significantly different outcomes over time. This concept highlights the sensitivity and complexity of chaotic systems, where minor variations in initial conditions can have a profound impact on the overall behavior and long-term predictions of the system.

The electrical force between an inner electron and the nucleus of an atom is determined by the distance between them and the charge of the nucleus. As the atomic number increases, the number of protons in the nucleus increases, resulting in a higher positive charge. This increased positive charge attracts the inner electrons more strongly, leading to a larger electrical force between the electron and the nucleus. Therefore, the electrical force is larger for atoms of high atomic number.

When an excited atom decays to its ground state, it emits a photon of green light. However, if the atom decays to an intermediate state, the energy difference between the excited state and the intermediate state may correspond to a different wavelength of light. In this case, the energy difference could correspond to red light, resulting in the emission of a red photon. Therefore, the light emitted could be red.

If atoms were smaller, it would mean that the particles within the atom, such as electrons and protons, would be closer together. Planck's constant, denoted as h, is a fundamental constant in quantum mechanics that relates the energy of a particle to its frequency. It is used to calculate the behavior of particles at the atomic and subatomic level. If the atoms were smaller, the particles within them would have a higher frequency and therefore a higher energy. This would result in a smaller value for Planck's constant.

Alpha particles are positively charged, consisting of two protons and two neutrons. Atomic nuclei also have positive charge due to the presence of protons. Since like charges repel each other, the repelling interaction between an alpha particle and the atomic nucleus occurs because they both have the same sign of electric charge.

The correct answer is "accounts for verified results of the old theory." This means that a new theory is considered to conform to the correspondence principle when it can explain and provide a rationale for the confirmed and established outcomes of the old theory. In other words, the new theory should be able to incorporate and justify the previously observed results of the old theory in order to be in line with the correspondence principle.

When alpha particles are fired through a gold foil, they bounce backward due to electrostatic repulsion when they come close to the gold nuclei. The positive charge of the alpha particles and the positive charge of the gold nuclei repel each other, causing the particles to change direction and bounce backward. This phenomenon is known as Rutherford scattering and was used by Ernest Rutherford in his gold foil experiment to discover the existence of the atomic nucleus.

Matter waves, also known as de Broglie waves, are associated with particles such as electrons or atoms. The wavelength of a matter wave is inversely proportional to the momentum of the particle. Since particles with small masses, such as electrons, have relatively high momenta, their matter waves have short wavelengths. On the other hand, visible light consists of photons with much larger masses, resulting in longer wavelengths. Therefore, compared to the wavelengths of visible light, the wavelengths of matter waves are relatively small.

The correct answer is "all of these." According to the correspondence principle, a new theory is considered valid if it overlaps and agrees with the old theory where it has been successful, accounts for confirmed results from the old theory, and predicts the same correct results as the old theory. In other words, a new theory should encompass and build upon the successes and findings of the old theory while also providing additional explanations and predictions.

Balmer, Rydberg, and Ritz discovered mathematical order in atomic spectra. This implies that there is a systematic pattern or relationship between the different energy levels or frequencies observed in the spectra of atoms. This finding suggests that there are underlying mathematical principles governing the behavior of electrons in atoms, which helps to understand the nature of atomic reality and the probabilities associated with different energy states.

The mass of an atom is directly proportional to its diameter. Since the uranium atom is 238 times as massive as a hydrogen atom, it can be inferred that the diameter of a uranium atom is also 238 times larger than that of a hydrogen atom. Therefore, the diameter of a uranium atom is the diameter of a hydrogen atom times about 3.

The diameter of an atom is determined by its atomic radius, which is the distance from the nucleus to the outermost electron shell. The atomic radius is typically measured in picometers (pm). In this question, we are comparing the diameters of a zirconium atom and a mercury atom. The atomic number (A) of zirconium is 40, and the atomic number of mercury is 80. Since the atomic number represents the number of protons in the nucleus, it can be inferred that the atomic radius of mercury is twice that of zirconium. However, the question asks for the comparison of the diameters, not the atomic radii. Since the diameter is twice the radius, the diameter of both atoms would be the same size.

The Schrödinger equation is not restricted to any specific type of particles. It is a fundamental equation in quantum mechanics that describes the behavior of particles, both microscopic and macroscopic. It is applicable to submicroscopic particles like electrons and protons, as well as larger particles like atoms and molecules. Therefore, the correct answer is "none of these".

In an atom with four distinct energy states, the number of possible spectral lines can be determined using the formula n(n-1)/2, where n is the number of energy states. Plugging in n=4, we get 4(4-1)/2 = 4(3)/2 = 12/2 = 6. Therefore, this atom can produce 6 spectral lines.

The correct answer is electric charge. Heavy atoms are not appreciably larger in size than light atoms because the nuclei of heavy atoms have more electric charge. The size of an atom is primarily determined by the number of electrons surrounding the nucleus, which is balanced by the positive charge of the protons in the nucleus. The electric charge of the nucleus affects the attraction between the electrons and the nucleus, but it does not directly determine the size of the atom. Therefore, the statement that heavy atoms are not larger in size than light atoms due to the electric charge of the nuclei is correct.

The correct answer is that the circumference of each orbit is an integral multiple of electron wavelengths. This is based on the concept of wave-particle duality in quantum mechanics. According to the de Broglie hypothesis, electrons exhibit wave-like behavior and have a wavelength associated with them. The circumference of the electron's orbit must be a whole number multiple of its wavelength in order for the electron's wave to form a complete standing wave around the nucleus. This restriction on the allowed orbits leads to the quantization of energy levels in an atom.

The correct answer is "none of these" because none of the given options accurately describe the discreteness of energy levels. The discreteness of energy levels is better understood through the concept of quantized energy levels, where electrons can only occupy specific energy levels in an atom. The options provided do not accurately represent this concept.