Chapter 6 Pt 1
After de Broglie proposed the wave nature of matter, Davisson and Germer demonstrated the wavelike behavior of electrons by observing an interference pattern from electrons scattering off what? Select the correct answer below: A single, microscopic aperture A nickel crystal A fine-toothed comb a beam of protons
Correct answer: A nickel crystal The small mass of an electron makes it among the easiest of particles (besides those with no mass, like photons) to observe the deBroglie wavelength. However, even with electrons, it is difficult to get the wavelength to be much longer than the size scale of an atom, so their experiment relied on the repeating pattern of a crystal to create an observable interference pattern.
What aspect of the classical mechanical description of the atom is flawed? Select the correct answer below: It predicts that an electron should be constantly emitting electromagnetic radiation. It predicts that an electron should continuously spiral into the nucleus. It predicts that atoms ought to be unstable. All of the above
Correct answer: All of the above All of the statements listed are predictions that classical mechanics make about the hydrogen atom, which is the paradox that demanded the work of Bohr.
In the equation for the orbital radii in hydrogen-like atoms, a0 is called the: Select the correct answer below: energy level Bohr radius nuclear charge orbital constant
Correct answer: Bohr radius The Bohr radius, a0 is equal to 5.292×10−11 m.
According to the Bohr model: Select the correct answer below: Electrons are constantly emitting electromagnetic radiation. Planck's ideas of quantization and Einstein's finding that light consists of photons whose energies are proportional to their frequency are not applicable. Continuous values are used for the angular momentum, energy, and orbit radius. Electrons only emit or absorb a photon if they move to a different orbit within the atom.
Correct answer: Electrons only emit or absorb a photon if they move to a different orbit within the atom. Bohr's model ignored the prediction that the orbiting electron in hydrogen would continuously emit light. He relied on Planck's and Einstein's work, and he used discrete values for angular momentum, energy, and orbit radius.
Who developed the wave equation of the electron? Select the correct answer below: Niels Bohr Louis de Broglie Erwin Schrodinger Werner Heisenberg
Correct answer: Erwin Schrodinger Schrodinger extended the work of de Broglie to develop the wave equation, and hence quantum mechanics.
Bohr's model of the hydrogen atom, which restricts electrons to circular orbits around the nucleus parameterized by a single number, n, can best be applied to which other species? Select the correct answer below: He H+ He+ Li+
Correct answer: He+ Bohr's model applies to any atom with one electron, such as He+,Li2+,Be3+, etc. Multielectron atoms like He are affected by repulsion between electrons and yield a more complicated pattern of energy levels.
Which of the following phenomena can only be explained by considering the wave nature of light? Select the correct answer below: Reflection Refraction Interference None of the above
Correct answer: Interference Early in the nineteenth century, Thomas Young demonstrated that light passing through narrow, closely spaced slits produced an interference pattern that could not be explained in terms of Newtonian particles, but could be easily explained in terms of waves. Phenomena such as reflection and refraction can be equally well explained in terms of light travelling as high-speed waves or as high-speed particles.
The Heisenberg uncertainty principle does not apply when measuring which pair of observable quantities? Select the correct answer below: The position or momentum of an electron. The kinetic energy and momentum of an electron. The vector components of angular momentum for an electron. The time required for an electron to undergo an energy transition and the change in the energy of the electron.
Correct answer: The kinetic energy and momentum of an electron. The Heisenberg Uncertainty Principle states that It is fundamentally impossible to determine simultaneously and exactly both the momentum and the position of a particle. Heisenberg's uncertainty principle is not just limited to uncertainties in position and momentum, but links other physical variables as well. For example, the uncertainty in the energy and the uncertainty in the time required for the transition are related to the Heisenberg Uncertainty Principle. For certain quantities, such as the kinetic energy and the momentum of an electron, the Heisenberg uncertainty principal does not not apply
Which will have the shortest wavelength for a given energy? Select the correct answer below: an electron a hydrogen atom a bacterium a baseball
Correct answer: a baseball The greater the mass of an object, the shorter its wavelength, as they are inversely proportional. So macroscopic objects have incredibly tiny wavelengths that are negligible, unlike subatomic particles.
Before the work of Albert Einstein and other prominent scientists of the early 1900's, the predominant view among physicists was that light is: Select the correct answer below: a particle a wave both a particle and a wave none of the above
Correct answer: a wave The predominant view before Einstein's work with the photoelectric effect was that light is wave. Scientists now recognize that light can behave as both a particle and a wave.
Bohr's model can be applied to which of the following? Select the correct answer below: Li2+ He+ Be3+ all of the above
Correct answer: all of the above Bohr's model can be applied to single electron ions such as He+,Li2+, and Be3+.
The first experimental evidence for the wave-like behavior of electrons supported de Broglie's model by demonstrating: Select the correct answer below: quantization of orbital energy the photoelectric effect an interference pattern for electrons reflecting off a crystal distribution of kinetic energy in electron collisions
Correct answer: an interference pattern for electrons reflecting off a crystal It was an interference pattern for electrons reflecting off a regular atomic pattern in a crystal that demonstrated the wave-like character of electrons, because such a pattern cannot be explained by corpuscular behavior.
The de Broglie expression can be rearranged to give quantization of: Select the correct answer below: orbital radius angular momentum orbital energy vibrational energy
Correct answer: angular momentum 2πr=nλ=nhp=nhmv=nhrmvr=nhrL This expression can be rearranged to show the formula for the quantinization of angular momentumL=nh2π=nℏ
The Schrödinger equation was developed directly from the: Select the correct answer below: Heisenberg uncertainty principle de Broglie relation Born's interpretation of the wavefunction none of the above
Correct answer: de Broglie relation Schrödinger incorporated the de Broglie relation into a wave equation to derive the equation that bears Schrödinger's name. In addition, when Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr's expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. The Heisenberg uncertainty principle indicates that it is impossible to know both the momentum and location of a particle simultaneously and Born's interpretation of the wavelengths followed a few years later.
When an electron moves from a lower, more stable orbit to a higher-energy orbit: Select the correct answer below: energy disrupts the discrete quantities of orbits energy is radiated through blackbodies energy is absorbed in the form of a photon energy is emitted in the form of a photon
Correct answer: energy is absorbed in the form of a photon When an electron moves from a lower, more stable orbit to a higher-energy orbit, energy is absorbed in the form of a photon.
When an electron moves from a higher-energy orbit to a more stable, lower energy orbit: Select the correct answer below: energy is absorbed in the form of a photon energy is radiated through blackbodies energy disrupts the discrete quantities of orbits energy is emitted in the form of a photon
Correct answer: energy is emitted in the form of a photon When an electron moves from a higher-energy orbit to a more stable, lower energy orbit, energy is emitted in the form of a photon.
When an electron moves from a higher-energy orbit to a more stable, lower energy orbit _____________ . Select the correct answer below: energy is absorbed in the form of a photon energy is radiated through blackbodies energy disrupts the discrete quantities of orbits energy is emitted in the form of a photon
Correct answer: energy is emitted in the form of a photon Work done by Bohr found that when an electron moves from a higher-energy orbit to a more stable, lower energy orbit, energy is emitted in the form of a photon. He found the energy absorbed or emitted would reflect differences in the orbital energies.
If an electron moves to an "excited state," this means Select the correct answer below: it has moved to an orbit with a lower n value. it has not moved to another orbit. it has moved to an orbit with a higher n value.
Correct answer: it has moved to an orbit with a higher n value. When an electron is said has become "excited" or moved to an "excited state," this indicates that the electron has been excited to an orbit that is higher than the ground state.
What was a severe limitation of Bohr's model for the atom? Select the correct answer below: it did not accurately predict any data it only worked for hydrogen atoms it only worked for one-electron systems it contradicted the work of Einstein
Correct answer: it only worked for one-electron systems Even when applied to the next smallest atom, a helium atom with two electrons, Bohr's model failed. It was still based on the classical mechanics notion of precise circular orbits, rather than the quantum mechanical principles that would soon follow.
That a photon of a particular energy must be emitted or absorbed when an electron in a hydrogen atom changes orbits is a ramification of the: Select the correct answer below: law of conservation of matter law of conservation of momentum law of conservation of charge law of conservation of energy
Correct answer: law of conservation of energy The electron will change its energy as it changes orbits, and thereby must emit a quantum of energy, or a photon, that is equivalent to this difference in orbital energy.
If mass and velocity are unknown when using de Broglie's wavelength formula, what alternative value must we have to successfully determine the wavelength? Select the correct answer below: tangential velocity angular momentum radius momentum
Correct answer: momentum de Broglie's wavelength formula is λ=hp or λ=hmv. Therefore if we are unable to determine mass and velocity, we must know the momentum of the particle.
The ground state for the hydrogen atom is represented by: Select the correct answer below: n=0 n=1 n=−1 n=∞
Correct answer: n=1 The ground state, which is the lowest possible energy, is n=1. It is followed by consecutive integers.
In the energy expression for hydrogen-like atoms, Z is equal to the: Select the correct answer below: atomic mass charge on the electron mass of the electron nuclear charge
Correct answer: nuclear charge The number of protons in the nucleus will be relevant in determining the energy of the electron, and it will be represented by the letter Z.
The angular momentum of an electron will be: Select the correct answer below: parallel to its orbit tangent to its orbit perpendicular to its orbit zero
Correct answer: perpendicular to its orbit The angular momentum of an object in circular motion, whether an electron or a macroscopic object, will be perpendicular to the plane of circular motion.
The model for the atom that was understood when Bohr made his contributions was called the: Select the correct answer below: planetary model plum pudding model solid sphere model quantum model
Correct answer: planetary model It was called the planetary model because it was thought that the electrons orbiting the nucleus must resemble planets orbiting a star.
Bohr theorized that the energy of an electron is _________, meaning that the electrons can have energies of particular values, but not any value from a continuous spectrum. Select the correct answer below: qualified concrete quantized obsolete
Correct answer: quantized Bohr theorized that the energy of an electron is quantized, meaning that the electrons can have energies of particular values, but not any value from a continuous spectrum.
When wave-particle duality was applied to the electron, it explained why the energy of the electron is quantized because: Select the correct answer below: the electron is a standing wave that can only have an integer number of wavelengths an electron can only exhibit specific velocities the electron must have a specific mass an electron will emit and absorb light quanta
Correct answer: the electron is a standing wave that can only have an integer number of wavelengths If the electron is viewed as a circular standing wave, it must be uninterrupted and therefore it must have an integer number of wavelengths and an integer number of nodes. This means it will have quantized energy.
Matter is most stable when it has _______ energy. Select the correct answer below: the highest possible fluctuating the lowest possible none of the above
Correct answer: the lowest possible Matter is most stable when it has the lowest possible energy. Electrons are most stable in their ground state because it is the lowest energy state.
Bohr used an electron moving in a circular orbit about a nucleus to describe: Select the correct answer below: the oscillation in electromagnetics the particle-like behavior of light the quantitative measures of discrete spectra the model of a hydrogen atom
Correct answer: the model of a hydrogen atom Bohr used an electron moving in a circular orbit about a nucleus to describe the model of a hydrogen atom.
Maxwell's theory of electromagnetic radiation was thought to have discredited which of the following? Select the correct answer below: the propagation of light the law of refraction the particle view of light none of the above
Correct answer: the particle view of light Maxwell's theory of electromagnetic radiation was thought to have discredited the particle view of light. James Clerk Maxwell showed that visible light was just a part of the vast electromagnetic spectrum, which includes many other forms of radiation.
The Heisenberg uncertainty principle states that there is a fundamental limit to how precisely both the position and momentum of electrons and other quantum particles can be known. This limit is due to _________. Select the correct answer below: the inability to see electrons limitations in mathematical models for momentum the wave-like nature of an electron the particle-like nature of an electron.
Correct answer: the wave-like nature of an electron Because the electron is so small, its behavior is heavily influenced by its wave-like properties. Particles have well defined positions and momenta, while waves do not. This uncertainty exists for all objects (even macroscopic) but only for extremely low mass particles like electrons does the uncertainty become large enough to affect measurements and predictions of particle behavior in any meaningful way.
If an electron emits a photon, it will also: Select the correct answer below: transition to a lower energy orbit transition to a higher energy orbit gain potential energy absorb a photon
Correct answer: transition to a lower energy orbit If an electron emits a photon of a particular energy, it will transition to a lower energy orbit in doing so, thus moving closer to the nucleus.
Which of the following is a form of electromagnetic radiation? Select the correct answer below: sound wave visible light mechanical wave none of the above
Correct answer: visible light Visible light is a form of electromagnetic radiation. Visible light and other forms of electromagnetic radiation are important because they can be used to infer the energies of electrons within atoms and molecules.
The view that light consists of both particles and waves is called: Select the correct answer below: combination model wave-particle duality light dualism wave-quanta combination
Correct answer: wave-particle duality The idea that light is made of both waves and particles is called wave-particle duality. This is the concept that every particle may be described not only in terms of particles but also of waves.
What is the calculated energy of an electron in a helium ion (He+) in an orbit with n=2? Use 2.18×10-18 J for the Rydberg constant (sometimes symbolized by k, RH, or R∞). Select the correct answer below: −5.44×10−18J −1.36×10−18J −2.18×10−18J −6.80×10−19J
Correct answer: −2.18×10−18J The energy of the electron is given by the following equation. E=−kZ2n2 Here, Z is the atomic number of helium, n is the quantum number of the orbital, and k is the Rydberg constant. The atomic number of helium is Z=2, we are given that k=2.18×10-18 J, and that electron is orbit with n=2. E=(−2.179×10−18 J)(2)2(2)2=−2.18×10−18 J
What is the energy of an electron in a hydrogen atom with an orbit of n=3? (k=2.18×10-18 J) Your answer should have three significant figures. When reporting your answer in scientific notation form, use the multiplication sign, ×, not the letter x.
Correct answers:$-2.42\times10^{-19}\text{ J}$−2.42×10−19 J E−(2.18×10−18J)(1)2(3)2=−kZ2n2=−2.42×10−19 J Notice that values for n (energy level occupied by the electron) and Z (atomic number) are exact, integer values, so they do not constrain the number of significant figures.
What is the energy of an electron in a helium ion (He+) in an energy level of n=4? Use 2.18×10-18 J for the Rydberg constant in joules (sometimes labeled Ry, R∞, or k). Report your answer in scientific notation. Your answer should be reported to three significant figures.
Correct answers:$-5.45\times10^{-19}\text{ J}$−5.45×10−19 J The energy of an electron in a single-electron ion or atom is given by the Rydberg equation (expressed here in units of energy): En=−kZ2n2 The atomic number, Z, of helium is 2; k=2.18×10-18 J; and the electron is characterized by an n value of 4. Thus,E=(−2.18×10−18 J)(2)242=−5.45×10−19 J Notice that values for n (energy level occupied by the electron) and Z (atomic number) are exact, integer values, so they do not constrain the number of significant figures.
A certain kind of light has a wavelength of 850 nm. What is the frequency of this light in Hz? Use c=2.998×108ms for the speed of light. Your answer should have two significant figures. When reporting your answer in scientific notation format, use the multiplication symbol, ×, not the letter x.
Correct answers:3.5×1014 Hz Recall that the useful wave equation is: c=λ⋅ν where λ is the wavelength, ν is the frequency, and c is the speed of light. First, convert the wavelength from nm to m: 850 nm×1 m109 nm=8.5×10−7 m Next, rearrange the equation to solve for ν: ν=cλ Substitute in the known values to solve: ν=2.998×108ms8.5×10−7 mν=3.53×1014 s−1 Note that Hertz (Hz) is another name for inverse seconds (s−1). The answer should have two significant figures, so round to 3.5×1014 Hz.
A certain kind of light has a wavelength of 4.6 μm (micrometers). What is the frequency of this light in GHz? Use c=2.998×108ms for the speed of light. Your answer should have two significant figures. When reporting your answer in scientific notation format, use the multiplication symbol, ×, not the letter x. Provide your answer below:
Correct answers:6.5×104 GHz Recall that the useful wave equation is: c=λ⋅ν where λ is the wavelength, ν is the frequency, and c is the speed of light. First, convert the wavelength from μm to m: 4.6μm×(1.0 m10.6 μm)=4.6×10−6 m Next, rearrange the equation to solve for ν: ν=cλ Substitute in the known values to solve: ν=2.998×108ms4.6×10−6 m=6.517×1013s−1 Convert the frequency to GHz. Remember that Hertz (Hz) is another name for inverse seconds (s−1). 6.517×1013 Hz(1.0 GHz1.0×109 Hz)=6.517×104 GHz Since the answer should have two significant figures, round to 6.5×104 GHz.
A laser emits light with a frequency of 4.75×1014 s−1. What is the wavelength of this radiation, in nm? Your answer should have three significant figures. Use c=2.998×108ms for the speed of light. Provide your answer below:
Correct answers:631 nm Recall that the useful wave equation is: c=λ⋅ν, where λ is the wavelength, ν is the frequency, and c is the speed of light. First, rearrange the equation to solve for λ: λ=cν Substitute in the known values to solve: λ=2.998×108ms4.75×1014 s−1λ=6.312×10−7 m Lastly, convert the wavelength from m to nm: 6.312×10−7 m×1.00×109 nm1.00 m=631.2 nm The answer should have three significant figures, so round to 631nm.
What is the wavelength of a wave with a frequency of 4.3 Hz? c=2.998×108 m s−1 Your answer should have two significant figures. Enter the answer in scientific notation. When reporting your answer in scientific notation format, use the multiplication symbol, ×, not the letter x.
Correct answers:7.0×107 m The equation is c=λ⋅v where c is the speed of light, λ is the wavelength, and v is the frequency. Note that 1Hz=1s−1. λ(4.3 s−1)=2.998×108 m s−1λ≈7.0×107 m
What is the energy of the He+ electron with n=4? (k=2.18×10−18 J) Your answer should have three significant figures. Provide your answer below:
Correct answers:−5.45×10−19 J En=−(kZ2n2)En=−(2.18×10−18)(22)42)En=−5.45×10−19 J
What is the energy of the electron in a helium ion with a charge of +1 in an orbit with a value of n=4? Use k=2.18×10−18J. Report your answer with three significant figures.
Correct answers:−5.45×10−19 J First, recall that the energy of the electron in a single-electron atom or ion is described by the equation: E=−kZ2n2 where k is the Rydberg constant (2.18×10−18 J), Z is the atomic number of the atom, and n is the energy level occupied by the electron. Substitute in the known values and solve: EE=−(2.18×10−18)(2)2(4)2=−5.45×10−19 J Notice that values for n (energy level occupied by the electron) and Z (atomic number) are exact, integer values, so they do not constrain the number of significant figures.