Chapter 7 Quiz - The Fundamental Nature Of Matter & Energy

The deBroglie wavelength of an object is given by the equation λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the object, and v is its velocity. In this case, the mass of the ball is given as 3.31 kg and its velocity is given as 1.00 m/s. Plugging these values into the equation, we get λ = (6.626 x 10^-34 J·s) / (3.31 kg x 1.00 m/s) = 2.00 x 10^-34 m.

The Heisenberg uncertainty principle states that an electron's exact location and velocity cannot be known with certainty. This principle is a fundamental concept in quantum mechanics and is a result of the wave-particle duality of electrons. According to the principle, the more accurately one tries to measure the position of an electron, the less accurately its velocity can be determined, and vice versa. This limitation arises from the inherent nature of quantum particles and the wave-like behavior of their wavefunctions. Therefore, it is impossible to simultaneously know both the exact position and velocity of an electron.

The correct answer is four-leaf-clover shaped. D orbitals have four lobes, each with a different orientation, giving them a shape similar to a four-leaf clover. This shape allows the d orbitals to have multiple orientations in space, which is important for their role in bonding and chemical reactions.

Hund's rule states that electrons cannot be placed randomly in orbitals. Instead, they must be paired until each orbital has an electron. This means that when filling the orbitals of an atom, each orbital must first have one electron before any of them can have a second electron. This rule helps to explain the observed electron configurations of atoms and the stability of their arrangements.

The 4th energy level of an atom can hold a maximum of 32 electrons. However, zirconium has an atomic number of 40, which means it has 40 electrons. To determine the number of electrons in the 4th energy level, we need to subtract the electrons in the previous energy levels. The first energy level can hold a maximum of 2 electrons, the second energy level can hold a maximum of 8 electrons, and the third energy level can hold a maximum of 18 electrons. Therefore, the number of electrons in the 4th energy level of a zirconium atom is 12.

The electron configuration given in the question corresponds to the element germanium. Germanium has an atomic number of 32, and its electron configuration is 1s22s22p63s23p64s23d104p2. This configuration represents the distribution of electrons in the different energy levels and orbitals of the atom.

The lowest part of a wave is called the trough. In a wave, the crest is the highest point, while the trough is the lowest point. The amplitude refers to the distance between the crest or trough and the rest position of the wave. Nadir, on the other hand, is a term used in astronomy to describe the lowest point reached by a celestial body in its orbit. Therefore, the correct answer is trough.

The ml value for an electron refers to its magnetic quantum number, which determines the orientation of the electron's orbital in space. It can have integer values ranging from -l to +l, where l is the azimuthal quantum number. In the case of an atom of aluminum, the unpaired electron is in the p orbital, which has an azimuthal quantum number of 1. Therefore, the ml value for this electron can be either -1, 0, or +1. However, since the question states that the electron is unpaired, it means that it is the only electron in its orbital. According to Hund's rule, when multiple orbitals of the same energy level are available, electrons will occupy separate orbitals with parallel spins before pairing up. In this case, the unpaired electron will occupy the p orbital with ml value of -1.

Scandium (Sc) is the correct answer because it is the only element among the options that has an electron configuration of 3d1. The quantum numbers provided in the question match the quantum numbers of the unpaired electron in scandium.

The frequency of an electromagnetic wave can be calculated using the formula: frequency = speed of light / wavelength. In this case, since the wavelength is given as 3.00 meters, we can substitute it into the formula to find the frequency. The speed of light is a constant value, so the frequency will be inversely proportional to the wavelength. Therefore, a longer wavelength will result in a lower frequency. Among the given options, 1.00 x 10^8 Hz has the lowest frequency and is the correct answer.

The energy of a photon can be calculated using the equation E = hf, where E is the energy, h is Planck's constant, and f is the frequency. In this question, the frequency of the electromagnetic wave is given as 1.00 x 10^10 Hz. Plugging this value into the equation, we get E = (6.63 x 10^-34 J.s)(1.00 x 10^10 Hz) = 6.63 x 10^-24 J. Therefore, the energy contained in one photon of this wave is 6.63 x 10^-24 J.

The quantum numbers n and l represent the energy level and the shape of an electron's orbital, respectively. The value of n must be a positive integer, while the value of l must be an integer ranging from 0 to (n-1). In this case, since n = 2 and l = 2, it is impossible because the value of l cannot exceed the value of n-1.

The 3d sublevel can hold a maximum of 5 orbitals. This is because the d sublevel has 5 orbitals (dxy, dyz, dzx, dx2-y2, and dz2) and each orbital can hold a maximum of 2 electrons. Therefore, the maximum number of orbitals in the 3d sublevel is 5.

When an electron moves from a higher energy level (n=5) to a lower energy level (n=6), it is undergoing a quantum leap. In this case, since the electron is moving to a higher energy level, it requires an absorption of energy. This is because energy is needed to move the electron against the attractive force of the nucleus.

The electron configuration given in the question is 1s22s22p63s23p64s23d4. This configuration corresponds to the element chromium (Cr), not vanadium (V) or manganese (Mn). Chromium has the electron configuration 1s22s22p63s23p64s23d4, which matches the given configuration. Therefore, the correct answer is none of the above.