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college physics reasoning

College Physics Reasoning and Relationships 2nd edition Nicholas Giordano - Solutions

Is the mass of a nucleus larger or smaller than the sum of the masses of the nucleons of which it is made? Explain.
What is (a) an alpha particle? (b) a beta particle? (c) a gamma ray? (d) an X-ray? (e) a daughter nucleus?
Was evidence for the nucleus first obtained through (a) Carbon dating, (b) The spectral lines of hydrogen, (c) Alpha particle scattering, (d) Cosmic rays, (e) Electromagnetic radiation
What is heavy water? Would an equal number of moles of heavy water actually weigh more than plain water?
Different isotopes of an element essentially share chemical properties. How, then, is it possible to separate different isotopes? Consider how one might use diffusion (Chapter 15) or a mass spectrometer (Chapter 20) (but not at the same time).
Why do different isotopes of a given element have, for most practical purposes, the same chemical properties? That is, why do different isotopes form the same molecules and compounds even though they have different numbers of neutrons and different masses?
As explained in Problem 61, TNT releases an energy of about 4.7 x 106 J/kg when it explodes. Assume an explosive could be designed using mostly hydrogen and releases an energy equal to approximately the binding energy of a hydrogen atom for each atom of explosive when it explodes. How much energy
One of the most powerful chemical explosives known is trinitrotoluene (TNT), which releases an energy of about 4.7 x 106 J for each kg of TNT that explodes. Is this energy at or near the limit of what is theoretically achievable with a chemical explosive? To estimate this limit, assume the
The process by which fi reflies glow, called bioluminescence, is defined as the emission of light from living organisms. In fireflies, bioluminescence occurs in cells called photocytes that are located in the last two segments of the abdomen. Fireflies produce light through a two-step chemical
The wavelength of the light from a sodium-vapor lamp is 589 nm. Assume a 100-W sodium-vapor lamp radiates its energy uniformly in all directions. (a) At what rate are photons emitted from the lamp? (b) At what distance from the lamp will the average flux of photons be 1 photon/(cm2s)? (c) What
LASIK, an acronym for laser-assisted in situ keratomileusis, is a form of laser eye surgery performed by ophthalmologists to correct myopia, hyperopia, and astigmatism. The procedure uses an excimer laser, which produces photons with a wavelength of 193 nm to remodel the corneal stroma. The photons
Suppose two hydrogen atoms, both initially in their ground state, are accelerated up to high speed and then collide head on. (a) Derive an expression for the speed necessary to raise both atoms to the same excited state, n. Assume all the initial kinetic energy goes into the energy of the
In a muonic atom, the electron is replaced by a negatively charged particle called a muon. The muon has the same charge as an electron, but its mass is 207 times the mass of an electron. Apply the Bohr model to a muonic hydrogen atom. (a) Calculate the radius of the orbit of the muon in the ground
Consider laser eye surgery, in which laser light with a wavelength of 514 nm at a power output of 1.5 W is used to reattach a detached retina. Suppose the laser is pulsed for 0.050-s time intervals. (a) During this time, how many photons are emitted by the laser? (b) What is the difference in
The Bohr model can be accurately applied to a singly ionized helium atom. This atom has two protons in the nucleus (Z = 2) and a single electron orbiting the nucleus. When the electron makes a transition from a higher energy level to the n = 4 level, some of these transitions produce light in the
Use the Bohr model to estimate the wavelength and frequency of the photon emitted during the n = 3 to n = 1 transition in molybdenum. The measured wavelength is 0.063 nm, which is different from the answer in part (a). What effects are omitted in the Bohr model that might explain why the Bohr model
The energy required to remove the “outermost” electron from a boron atom is 8.26 eV. As an approximation, you can model the quantum state of this electron as that of a single electron in a hydrogen atom, but with an “effective” charge on the nucleus that is different from the charge of a
Suppose a hydrogen atom is in the 6h state. Determine (a) the principal quantum number, (b) the energy of the state, (c) the orbital angular momentum and its quantum number l. (d) the possible values for the magnetic quantum number.
Suppose the electron spin had three possible values instead of two. For this situation, determine the electron configuration of the ground state of a lithium atom. Assume all electrons must be in different quantum states (i.e., have different quantum numbers).
Imagine that electron spin did not exist. (a) How many electrons would occupy the 1s state? Why? (b) If there were no electron spin, what would be the first two noble gases in the periodic table?
For each of the following ground-state electron configurations, identify the atom.(a) 1s22s22p6(b) 1s22s22p63s23p4(c) 1s22s2
How many different quantum states are there for electrons in the subshells with (a) l = 0, (b) l = 2,(c) l = 3?
(a) How many different quantum states are there for electrons in the n = 3 shell? That is, how many different unique quantum numbers are there for an electron in the n = 3 shell? (b) Write the explicit values of all the quantum numbers (n, l, m, s) for electrons in this shell.
Using the Bohr model of the hydrogen atom, show that the speed of an electron in an orbit is given by vn = (2.2 x 106)/n m/s. Here n is the quantum number in the Bohr model.
Consider a hydrogen atom in its n = 5 state. Suppose it decays to the n = 2 state before proceeding to its ground state. (a) Determine the wavelengths of the emitted photons. (b) To what region of the electromagnetic spectrum do these photons correspond?
Determine the dissociation energy for hydrogen’s electron for the states with the following principal quantum number: (a) n = 2, (b) n = 10, (c) n = 100.
Scientists are able to study atoms much larger than a hydrogen atom in its ground state. Consider a hydrogen atom with n = 200. (a) Determine the diameter of this atom (i.e., the diameter of this Bohr orbit). (b) Compare the diameter of this atom to that of a dust particle (about 10-6 m).
Consider an electron in the n = 1 state hydrogen. (a) Find the speed v of this electron and the radius r of its orbit in the Bohr model. (b) What is the time needed for the electron to complete one orbit? (c) This orbiting electron acts as a current loop. What is the value of the current? (d)
When an atom undergoes a transition from one level to another, the energy needed is usually provided by a photon, but it may also come from the kinetic energy of a collision. Consider the collision of two hydrogen atoms, one with an initial speed v and another initially at rest. What value of v is
We applied the Bohr model to hydrogen, but it can be extended to treat ions with one electron such as He+ and Li+2. Follow the derivation in Equations 29.10 through 29.15, but now let the nucleus have a charge +Ze (for a nucleus with atomic number Z containing Z protons) instead of just +e (a
A ruby laser uses the photons emitted by Cr+3 ions that are embedded in a crystal of Al2O3 (instead of in a gas, as with a helium–neon laser). The light emitted by a ruby laser has a wavelength of approximately 694 nm. (a) What is the frequency of this light? (b) What is the spacing, in
Most helium–neon lasers emit visible light with a wavelength of 633 nm. These lasers can also emit photons in the infrared with a wavelength of 1.15 mm. What is the frequency of these photons?
Which elements have chemical properties similar to calcium (Ca)?
List all the known elements whose chemical properties are similar to those of fluorine (F).
How many electrons can occupy (a) The 3d subshell, (b) The 5s subshell, (c) The n = 4 shell, (d) The 4f subshell, (e) The 5g subshell, (f) Any h subshell
Give the electron configurations of the following atoms in their ground states: (a) Ge, (b) Ar, (c) Mg, (d) Si, (e) Br.
How many electrons are in (a) the 4p subshell of Br, (b) the n = 4 shell of Rb, (c) the 4f subshell of U, and (d) the 3d subshell of Cs?
Identify the following neutral atoms from their electron configurations.(a) 1s22s22p63s23p63d104s1(b) 1s22s22p63s23p63d104s24p5(c) 1s22s22p63s23p63d104s24p65s2
A neutral atom has the electron configuration 1s22s22p63s23p3. What element is it?
An electron is in a subshell that contains 18 states. What is the value of l?
What are the allowed values of l, for electrons in the n = 5 shell?
What is the total number of electron states in the n = 3 shell?
How many electron states in the hydrogen atom have the quantum numbers (a) n = 2 and ,l = 1? (b) n = 3 and , l = 2?
A hydrogen atom in its ground state absorbs a photon with an energy of 21.0 eV, and the electron is ejected. What is the kinetic energy of the ejected electron?
(a) What is the energy of the n = 5 state of hydrogen? (b) A hydrogen atom that is initially in some unknown state (i.e., the atom is not ionized and the value of n is not known) undergoes a transition and ends up in the n = 5 state. What is the highest energy photon that can possibly be
The radius of an electron orbit in the Bohr model depends on the value of n. (a) Find the value of n for which r =1μm. These atoms are called Rydberg atoms. This orbit is relatively large; objects of this size are visible with an optical microscope. (b) Find the energy.
Calculate the de Broglie wavelength of an electron in the n = 3 state of hydrogen. Is this wavelength larger or smaller than for the n = 1 state?
Find the de Broglie wavelength for an electron in the n = 1 state of hydrogen.
A hydrogen atom emits a photon of energy about 2.55 eV. What are the values of n for the initial and final states involved in this transition?
What is the energy needed to cause an electron to undergo a transition from the n = 3 state to the n = 5 state in hydrogen?
A hydrogen atom in the ground state absorbs a photon with an energy of approximately 12.8 eV. What is the value of n for the final state of the atom?
In the Bohr model of a hydrogen atom, what is the electric force exerted between the proton and the electron when (a) The electron is in the n = 1 state (b) The electron is in the n = 5 state?
(a) How much energy is needed to ionize a hydrogen atom that is initially in its n = 4 state? (b) In what region of the electromagnetic spectrum does this photon fall? If it is in the visible portion of the spectrum, what color does this photon correspond to?
What is the smallest energy photon that can be absorbed by a hydrogen atom in its ground state? In what region of the electromagnetic spectrum does this photon fall? If it is in the visible portion of the spectrum, what color does this photon correspond to?
Find the energy of an electron in the n = 3 state of hydrogen. If this electron undergoes a transition to the ground state, what is the energy, in electron-volts, of the photon that is emitted?
According to the Bohr model, what is the orbital radius of an electron in the n = 10 state of hydrogen?
What is the minimum frequency a photon can have so as to ionize a hydrogen atom? Assume the atom begins in its ground state.
A hypothetical atom absorbs photons at the following energies (all given in electron-volts): 2.0, 4.0, 6.0, 8.0, and 10.0. Construct an energy-level diagram that explains this spectrum.
An atom emits photons with an energy of 2.5 eV. (a) What is the spacing, in joules, between the energy levels involved in this atomic transition? (b) Where are these photons in the electromagnetic spectrum (i.e., infrared, visible, ultraviolet)?
Suppose a hydrogen atom was somehow enlarged so that the nucleus is the size of a baseball (diameter approximately 8 cm). What is the approximate diameter of the volume occupied by the orbit of the electron in the planetary model? How does it compare with the diameter of the Earth?
The nucleus of a hydrogen atom is a single proton. The radius of a proton is approximately 1 fm (1x1015 m). (a) What is the approximate volume of a proton? (b) A hydrogen atom has an approximate radius of 5x 1011 m (called the Bohr radius). What is the approximate volume of a hydrogen atom? (c)
When illuminated with ultraviolet light, many minerals glow in the visible part of the electromagnetic spectrum. Why?
What experiment would you do to determine if there is oxygen in the atmosphere of a planet going around a distant star?
What experiment would you do to determine if there is oxygen in a distant star?
What would the spectrum of hydrogen look like if the electrons could move between orbits of any radius in Bohr’s model?
Explain why it is difficult to chemically separate the elements Ce (cerium) through Lu (lutitium) from each other. Hint: Consider the electrons that determine the bonding properties of these atoms. What states do these electrons occupy?
Explain how the elements Cr through Cu in the periodic table can have fairly similar chemical properties, even though they are not arranged in the same column of the periodic table.
Neon is one of many gases that emit light when exposed to electrodes across which there is a large electric potential difference. Neon bulbs emit red light, but other gases emit other colors. Use the Internet to look up what kinds of atoms are used in bulbs that emit red, green, blue, and yellow
Derive a general expression for the de Broglie wavelength of an electron for the Bohr model in state n.
Explain why the Pauli exclusion principle is not needed to understand the allowed quantum states of the electron in a hydrogen atom.
Explain why He, Ne, Ar, and Kr rarely form stable molecules.
Explain why F, Cl, and Br have similar chemical properties.
Show that 4l+2 electrons can occupy a subshell with orbital quantum number l.
In the Bohr model, the total energy of an electron in the ground state in the hydrogen atom is -13.6 eV. Explain why this energy is negative.
Explain why Rutherford’s planetary model of the atom is inconsistent with classical physics and what we know about atoms.
Explain why the plum-pudding model of the atom is inconsistent with experimental results.
Of the following configurations, which ones are not allowed for the outermost shell of an atom by quantum theory, (a) 4s4, (b) 3d7, (c) 4f9, or (d) 2d3? Explain why not.
Is there an upper limit to the wavelength of light that a hydrogen atom can emit? Explain why or why not.
Consider the He+ ion. Like a hydrogen atom, He+ has one electron, but it has two protons, so the charge of the nucleus is +2e. Do you expect the ionization energy of He+ to be greater than or less than that of H? Explain.
Explain why some periodic tables list H twice, once above Li and again above the column containing F.
Explain why He, Ne, and Ar have similar chemical properties.
A normal CD player uses a laser with λ = 5 780 nm, whereas a Blu-ray player uses a laser with a shorter wavelength, λ = 405 nm. (These values are the wavelengths in air; the wavelengths are shorter in the plastic of each disc.) If the lasers in a CD player and a Blu-ray player have the same
The intensity of the Sun at the Earth’s surface is approximately 1000 W/m2. Estimate the number of photons from the Sun that strike an area of 1 m2 each second.
A “mosquito push-up” is the work done by a mosquito when it lifts its body (m ≈ 1 milligram) through a distance of 1 mm (the approximate length of a mosquito’s “arms”). This amount of mechanical energy is very small. (a) How many mosquito pushups does it take to equal the energy in a
Microwave ovens operate at a wavelength of 12.24 cm and have a typical output of 700 W. (a) How many photons are emitted by the oven’s microwave generator per second? (b) Approximately what is the minimum number of photons needed to heat a cup of coffee or tea (mostly water) from 25°C to 90°C?
(a) Calculate the electric potential difference needed to accelerate a proton so that it has a wavelength of 1.0x10-12 m. (b) Repeat the calculation for an electron. Here you must use the relativistic expressions for energy and momentum. (c) Compare the energies of these two particles (ratio of
In the mid 1960s, the Stanford Linear Accelerator was the first to attain the ability to accelerate electrons to a kinetic energy of 20 GeV (giga-electron-volts). A series of experiments involved directing the beam of electrons at protons. By examining the angular distribution of the electrons
Consider the following two quantum processes, each of which always emits a photon of a specific wavelength: (1) a 1.45-nm gamma ray from the nuclear process of cobalt-56 radioactive decay and (2) the 546-nm photon from the de-excitation of mercury in a street lamp (in the regime of chemical binding
The threshold intensity for a human eye to sense the presence of light is 50 photons falling on the retina within a period of 0.1 s. The Sun radiates an output of 2.0x1026 W in the visible wavelengths, with a peak at λ = 550 nm. Estimate how far away a star like the Sun can be and still be visible
The mass of a mosquito is about 1 milligram. If its speed is 2 m/s, what is its wavelength?
(a) What is the de Broglie wavelength of a helium atom with kinetic energy 2.0 eV? (b) At what energy would the wavelength be approximately equal to the spacing between atoms in a crystal? This condition is usually a requirement for observing diffraction of a wave from the atoms in a crystal.
A photoelectric experiment uses light with a wavelength λ = 550 nm, and the ejected electrons are found to have a kinetic energy of 0.25 eV. What is the work function of the metal?
Given that the threshold for a human eye to sense the presence of light is 50 photons within 0.1 s, what is the minimum power output of a red (λ = 635 nm) laser diode that would make it visible in a darkened room?
Consider a hypothetical STM in which the tunneling particles are protons instead of electrons. Assuming an electron STM has a tunneling gap of 0.5 nm, estimate the size of the gap required for a proton STM. Assume all other parameters (including the kinetic energy) are the same.
A beam of electrons is directed along the x axis and through a slit that is parallel to the y axis and 10 mm wide. The electrons then continue on to a screen 1.5 m away. The electrons in the beam have a kinetic energy of 70 eV. (a) What is the de Broglie wavelength of the electrons? (b) What is
Suppose an electron is confined to a region of width 10 nm. The electron wave function forms a standing wave with nodes at the ends of the region. (a) What is the lowest-energy electron that can form such a standing wave? (b) What is the energy of an electron that forms a standing wave with three
Use the Heisenberg uncertainty relation to find the approximate kinetic energy of an electron that is trapped in a region the size of an atomic nucleus (1 fm = 1x10-15 m). Is this electron moving relativistically?
A proton in an atom is confined to the nucleus, which has a diameter of approximately 1 fm (1x10-15 m). This diameter is also the uncertainty Δx in the proton’s position. Compute the uncertainty in the proton’s momentum. What is the corresponding kinetic energy of the proton? We’ll use this
An atom has a size of approximately 0.1 nm. Take this size as Δx, the uncertainty in the position of an electron in the atom. (a) Use the Heisenberg uncertainty relation to compute the uncertainty Δp in the electron’s momentum. (b) If the electron’s total momentum is equal to Δp, what is
If an electron is confined to a region of size 1.0 nm, what is the minimum possible uncertainty in its momentum?

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