What are the wavelengths of spectral lines in the Balmer

How do we learn about light and matter?

How is light emitted and absorbed?

How do we know that atoms have smaller parts?

What is Rutherfords model of the atom?

What is inside the atomic nucleus?

Why are atoms important?

What are the peak wavelengths and the corresponding spectral regions for thermal radiation from the sun, a glowing ball of gas with a surface temperature of 5800 K, and from the earth, whose average surface temperature is 15C?

These spectra are due to the same element. Which one is an emission spectrum and which is an absorption spectrum?

An electron is fired between two parallel-plate electrodes that are 5.0 mm apart and 3.0 cm long. A potential difference V between the electrodes establishes an electric field between them. A 3.0-cm-wide, 1.0 mT magnetic field overlaps the electrodes and is perpendicular to the electric field. When V = 0 V, the electron is deflected by 2.0 mm as it passes between the plates. What value of V will allow the electron to pass through the plates without deflection?

Thomsons conclusion that cathode-ray particles are fundamental constituents of atoms was based primarily on which observation? a. They have a negative charge. b. They are the same from all cathode materials. c. Their mass is much less than that of hydrogen. d. They penetrate very thin metal foils.

Oil has a density of 860 kg/m3 . A 1.0@mm@diameter oil droplet acquires 10 extra electrons as it is sprayed. What potential difference between two parallel plates 1.0 cm apart will cause the droplet to be suspended in air?

A radioactive nucleus undergoes alpha decay. Between leaving the nucleus and reaching the laboratory, the alpha particle a. Speeds up. b. Slows down. c. First speeds up, then slows down. d. Travels at constant speed.

An alpha particle is shot with a speed of 2.0 * 107 m/s directly toward the nucleus of a gold atom. What is the distance of closest approach to the nucleus?

Carbon is the sixth element in the periodic table. How many electrons are in a C++ ion?

Alpha particles are usually characterized by their kinetic energy in MeV. What is the speed of an 8.3 MeV alpha particle?

Carbon is the sixth element in the periodic table. How many protons and how many neutrons are there in a nucleus of the isotope 14 C?

In a simple model of the hydrogen atom, the electron orbits the proton at 2.19 * 106 m/s in a circle with radius 5.29 * 10-11 m. What is the atoms energy in eV?

What is the minimum energy required to ionize a hydrogen atom?

The cesium isotope 137 Cs, with Z = 55, is radioactive and decays by beta decay. A beta particle is observed in the laboratory with a kinetic energy of 300 keV. With what kinetic energy was the beta particle ejected from the 12.4-fm-diameter nucleus?

A brass plate at room temperature radiates 10 W of blackbody radiation. If the plate is cooled to 30C, does the peak of maximum radiated intensity shift toward shorter wavelengths, shift toward longer wavelengths, or remain the same? Explain

a. Summarize the experimental evidence prior to the research of Thomson by which you might conclude that cathode rays are some kind of particle. b. Summarize the experimental evidence prior to the research of Thomson by which you might conclude that cathode rays are some kind of wave.

Thomson observed deflection of the cathode-ray particles due to magnetic and electric fields, but there was no observed deflection due to gravity. Why not?

What was the significance of Thomsons experiment in which an off-center electrode was used to collect charge deflected by a magnetic field?

What is the evidence by which we know that an electron from an iron atom is identical to an electron from a copper atom?

FIGURE Q37.6 shows a magnetic field between two parallel, charged electrodes. An electron with speed v0 passes between the plates, from left to right, with no deflection. If a proton is fired toward the plates with the same speed v0, will it be deflected up, deflected down, or pass through with no deflection? Explain.

a. Describe the experimental evidence by which we know that the nucleus is made up not just of protons. b. The neutron is not easy to isolate or control because it has no charge that would allow scientists to manipulate it. What evidence allowed scientists to determine that the mas

Rutherford studied alpha particles using the crossed-field technique Thomson had invented to study cathode rays. Assuming that valpha vcathode ray (which turns out to be true), would the deflection of an alpha particle by a magnetic field be larger than, smaller than, or the same as the deflection of a cathode-ray particle by the same field? Explain

Once Thomson showed that atoms consist of very light negative electrons and a much more massive positive charge, why didnt physicists immediately consider a solar-system model of electrons orbiting a positive nucleus? Why would physicists in 1900 object to such a model?

Explain why the observation of alpha particles scattered at very large angles led Rutherford to reject Thomsons model of the atom and to propose a nuclear model

An alpha particle (a bare helium nucleus with q = +2e) accelerates across a 100 V potential difference, starting from rest. What is the particles kinetic energy in eV when it reaches the negative electrode? This question requires no mathematics beyond what you can do in your head.

Identify the element, the isotope, and the charge state of each atom in FIGURE Q37.12. Give your answer in symbolic form, such as 4 He+ or 8 Be-.

What are the wavelengths of spectral lines in the Balmer series with n = 6, 8, and 10?

Figure 37.7 identified the wavelengths of four lines in the Balmer series of hydrogen. a. Determine the Balmer formula n and m values for these wavelengths. b. Predict the wavelength of the fifth line in the spectrum

The wavelengths in the hydrogen spectrum with m = 1 form a series of spectral lines called the Lyman series. Calculate the wavelengths of the first four members of the Lyman series

Two of the wavelengths emitted by a hydrogen atom are 102.6 nm and 1876 nm.a. What are the m and n values for each of these wavelengths? b. For each of these wavelengths, is the light infrared, visible, or ultraviolet?

A 2.0-cm-diameter metal sphere is glowing red, but a spectrum shows that its emission spectrum peaks at an infrared wavelength of 2.0 mm. How much power does the sphere radiate? Assume e = 1

What temperature, in C, is a blackbody whose emission spectrum peaks at (a) 300 nm and (b) 3.00 mm?

A ceramic cube 3.0 cm on each side radiates heat at 630 W. At what wavelength, in mm, does its emission spectrum peak? Assume e = 1.

The current in a Crookes tube is 10 nA. How many electrons strike the face of the glass tube each second?

Electrons pass through the parallel electrodes shown in FIGURE EX37.9 with a speed of 5.0 * 106 m/s. What magnetic field strength and direction will allow the electrons to pass through without being deflected? Assume that the magnetic field is confined to the region between the electrodes.

An electron in a cathode-ray beam passes between 2.5-cmlong parallel-plate electrodes that are 5.0 mm apart. A 2.0 mT, 2.5-cm-wide magnetic field is perpendicular to the electric field between the plates. The electron passes through the electrodes without being deflected if the potential difference between the plates is 600 V. a. What is the electrons speed? b. If the potential difference between the plates is set to zero, what is the electrons radius of curvature in the magnetic field?

An oil droplet with 15 excess electrons is observed between two parallel electrodes spaced 12 mm apart. The droplet hangs motionless if the upper electrode is 25 V more positive than the lower electrode. The density of the oil is 860 kg/m3 . What is the radius of the droplet?

A 0.80@mm@diameter oil droplet is observed between two parallel electrodes spaced 11 mm apart. The droplet hangs motionless if the upper electrode is 20 V more positive than the lower electrode. The density of the oil is 885 kg/m3 . a. What is the droplets mass? b. What is the droplets charge? c. Does the droplet have a surplus or a deficit of electrons? How many?

Suppose that in a hypothetical oil-drop experiment you measure the following values for the charges on the drops: 3.99 * 10-19 C, 6.65 * 10-19 C, 2.66 * 10-19 C, 10.64 * 10-19 C, and 9.31 * 10-19 C. What is the largest value of the fundamental unit of charge that is consistent with your measurements?

Determine: a. The speed of a 7.0 MeV neutron. b. The speed of a 15 MeV helium atom. c. The specific type of particle that has 1.14 keV of kinetic energy when moving with a speed of 2.0 * 107 m/s.

Determine: a. The speed of a 300 eV electron. b. The speed of a 3.5 MeV H+ ion. c. The specific type of particle that has 2.09 MeV of kinetic energy when moving with a speed of 1.0 * 107 m

Express in eV (or keV or MeV if more appropriate): a. The kinetic energy of a Li ++ ion that has accelerated from rest through a potential difference of 5000 V. b. The potential energy of two protons 10 fm apart. c. The kinetic energy, just before impact, of a 200 g ball dropped from a height of 1.0 m

Express in eV (or keV or MeV if more appropriate): a. The kinetic energy of an electron moving with a speed of 5.0 * 106 m/s. b. The potential energy of an electron and a proton 0.10 nm apart. c. The kinetic energy of a proton that has accelerated from rest through a potential difference of 5000 V.

A parallel-plate capacitor with a 1.0 mm plate separation is charged to 75 V. With what kinetic energy, in eV, must a proton be launched from the negative plate if it is just barely able to reach the positive plate?

How many electrons, protons, and neutrons are contained in the following atoms or ions: (a) 10 B, (b) 13 N+, and (c) 17 O+++?

Identify the isotope that is 11 times as heavy as 12 C and has 18 times as many protons as 6 Li. Give your answer in the form A S, where S is the symbol for the element. See Appendix C: Atomic and Nuclear Data

Write the symbol for an atom or ion with: a. one electron, one proton, and two neutrons. b. seven electrons, eight protons, and ten neutrons

Write the symbol for an atom or ion with: a. five electrons, five protons, and six neutrons. b. five electrons, six protons, and eight neutrons.

Consider the gold isotope 197 Au. a. How many electrons, protons, and neutrons are in a neutral 197 Au atom? b. The gold nucleus has a diameter of 14.0 fm. What is the density of matter in a gold nucleus? c. The density of lead is 11,400 kg/m3 . How many times the density of lead is your answer to part b?

Consider the lead isotope 207 Pb. a. How many electrons, protons, and neutrons are in a neutral 207 Pb atom? b. The lead nucleus has a diameter of 14.2 fm. What is the electric field strength at the surface of a lead nucleus?

a. A 238 U nucleus has a radius of 7.4 fm. What is the density, in kg/m3 , of the nucleus? b. A neutron star consists almost entirely of neutrons, created when electrons and protons are squeezed together under immense gravitational pressure, and it has the density of an atomic nucleus. What is the radius, in km, of a neutron star with the mass of the sun?

What is the total energy, in MeV, of a. A proton traveling at 99% of the speed of light? b. An electron traveling at 99% of the speed of light? Hint: This problem uses relativity

What is the velocity, as a fraction of c, of a. A proton with 500 GeV total energy? b. An electron with 2.0 GeV total energy? Hint: This problem uses relativity

The Large Hadron Collider accelerates two beams of protons, which travel around the collider in opposite directions, to a total energy of 6.5 TeV per proton. 11 TeV = 1 teraelectron volt = 1012 eV.2 The beams cross at several points, and a few protons undergo headon collisions. Such collisions usually produce many subatomic particles, but in principle the colliding protons could produce a single subatomic particle at rest. (It would be unstable and would almost instantly decay into other subatomic particles.) What would be the mass, as a multiple of the protons mass, of such a particle? Hint: This problem uses relativity.

The Large Hadron Collider accelerates protons to a total energy of 6.5 TeV per proton. 11 TeV = 1 teraelectron volt = 1012 eV.2 What is the speed of a proton that has this energy? Give your answer as fraction of c, using as many significant figures as needed. Hint: This problem uses relativity.

You learned in Chapter 36 that mass has an equivalent amount of energy. What are the energy equivalents in MeV of the rest masses of an electron and a proton?

The factor g appears in many relativistic expressions. A value g = 1.01 implies that relativity changes the Newtonian values by approximately 1% and that relativistic effects can no longer be ignored. At what kinetic energy, in MeV, is g = 1.01 for (a) an electron, (b) a proton, and (c) an alpha particle?

The fission process n + 235 U S 236 U S 144 Ba + 89 Kr + 3n converts 0.185 u of mass into the kinetic energy of the fission products. What is the total kinetic energy in MeV?

An electron in a cathode-ray beam passes between 2.5-cmlong parallel-plate electrodes that are 5.0 mm apart. A 1.0 mT, 2.5-cm-wide magnetic field is perpendicular to the electric field between the plates. If the potential difference between the plates is 150 V, the electron passes through the electrodes without being deflected. If the potential difference across the plates is set to zero, through what angle is the electron deflected as it passes through the magnetic field?

The two 5.0-cm-long parallel electrodes in FIGURE P37.34 are spaced 1.0 cm apart. A proton enters the plates from one end, an equal distance from both electrodes. A potential difference V = 500 V across the electrodes deflects the proton so that it strikes the outer end of the lower electrode. What magnetic field strength and direction will allow the proton to pass through undeflected while the 500 V potential difference is applied? Assume that both the electric and magnetic fields are confined to the space between the electrodes.

An unknown charged particle passes without deflection through crossed electric and magnetic fields of strengths 187,500 V/m and 0.1250 T, respectively. The particle passes out of the electric field, but the magnetic field continues, and the particle makes a semicircle of diameter 25.05 cm. What is the particles charge-to-mass ratio? Can you identify the particle?

In one of Thomsons experiments he placed a thin metal foil in the electron beam and measured its temperature rise. Consider a cathode-ray tube in which electrons are accelerated through a 2000 V potential difference, then strike a 10 mg copper foil. What is the electron-beam current if the foil temperature rises 6.0C in 10 s? Assume no loss of energy by radiation or other means. The specific heat of copper is 385 J/kgK

A neutral lithium atom has three electrons. As you will discover in Chapter 41, two of these electrons form an inner core, but the thirdthe valence electronorbits at much larger radius. From the valence electrons perspective, it is orbiting a spherical ball of charge having net charge +1e (i.e., the three protons in the nucleus and the two inner-core electrons). The energy required to ionize a lithium atom is 5.14 eV. According to Rutherfords nuclear model of the atom, what are the orbital radius and speed of the valence electron? Hint: Consider the energy needed to remove the electron and the force needed to give the electron a circular orbit

A hydrogen atom 1 H with 200 eV of kinetic energy has a headon, perfectly elastic collision with a 12 C atom at rest. Afterward, what is the kinetic energy, in eV, of each atom?

The diameter of an atom is 1.2 * 10-10 m and the diameter of its nucleus is 1.0 * 10-14 m. What percent of the atoms volume is occupied by mass and what percent is empty space?

The diameter of an aluminum atom of mass 27 u is approximately 1.2 * 10-10 m. The diameter of the nucleus of an aluminum atom is approximately 8 * 10-15 m. The density of solid aluminum is 2700 kg/m3 . a. What is the average density of an aluminum atom? b. Your answer to part a was larger than the density of solid aluminum. This suggests that the atoms in solid aluminum have spaces between them rather than being tightly packed together. What is the average volume per atom in solid aluminum? If this volume is a sphere, what is the radius? Hint: The volume per atom is not the same as the volume of an atom. c. What is the density of the aluminum nucleus? By what factor is the nuclear density larger than the density of solid aluminum?

A 222 Rn atom (radon) in a 0.75 T magnetic field undergoes radioactive decay, emitting an alpha particle in a direction perpendicular to B u . The alpha particle begins cyclotron motion with a radius of 45 cm. With what energy, in MeV, was the alpha particle emitted?

The polonium isotope 211 Po is radioactive and undergoes alpha decay. In the decay process, a 211 Po nucleus at rest explodes into an alpha particle (a 4 He nucleus) and a 207 Pb lead nucleus. The lead nucleus is found to have 0.14 MeV of kinetic energy. The energy released in a nuclear decay is the total kinetic energy of all the decay products. How much energy is released, in MeV, in a 211 Po decay?

In a head-on collision, the closest approach of a 6.24 MeV alpha particle to the center of a nucleus is 6.00 fm. The nucleus is in an atom of what element? Assume the nucleus remains at res

Through what potential difference would you need to accelerate an alpha particle, starting from rest, so that it will just reach the surface of a 15-fm-diameter 238 U nucleus?

The oxygen nucleus 16 O has a radius of 3.0 fm. a. With what speed must a proton be fired toward an oxygen nucleus to have a turning point 1.0 fm from the surface? Assume the nucleus remains at rest. b. What is the protons kinetic energy in MeV?

To initiate a nuclear reaction, an experimental nuclear physicist wants to shoot a proton into a 5.50-fm-diameter 12 C nucleus. The proton must impact the nucleus with a kinetic energy of 3.00 MeV. Assume the nucleus remains at rest. a. With what speed must the proton be fired toward the target? b. Through what potential difference must the proton be accelerated from rest to acquire this speed?

An alpha particle approaches a 197 Au nucleus with a speed of 1.50 * 107 m/s. As FIGURE CP37.47 shows, the alpha particle is scattered at a 49 angle at the slower speed of 1.49 * 107 m/s. In what direction does the 197 Au nucleus recoil, and with what speed?

Physicists first attempted to understand the hydrogen atom by applying the laws of classical physics. Consider an electron of mass m and charge -e in a circular orbit of radius r around a proton of charge +e. a. Use Newtonian physics to show that the total energy of the atom is E = -e2 /8pP0r. b. Show that the potential energy is -2 times the electrons kinetic energy. This result is called the virial theorem. c. The minimum energy needed to ionize a hydrogen atom (i.e., to remove the electron) is found experimentally to be 13.6 eV. From this information, what are the electrons speed and the radius of its orbit?

Consider an oil droplet of mass m and charge q. We want to determine the charge on the droplet in a Millikan-type experiment. We will do this in several steps. Assume, for simplicity, that the charge is positive and that the electric field between the plates points upward. a. An electric field is established by applying a potential difference to the plates. It is found that a field of strength \(E_0\) will cause the droplet to be suspended motionless. Write an expression for the droplet’s charge in terms of the suspending field \(E_0\) and the droplet's weight mg. b. The field \(E_0\) is easily determined by knowing the plate spacing and measuring the potential difference applied to them. The larger problem is to determine the mass of a microscopic droplet. Consider a mass m falling through a viscous medium in which there is a retarding or drag force. For very small particles, the retarding force is given by \(F_{drag} = -bv\) where b is a constant and v the droplets velocity. The sign recognizes that the drag force vector points upward when the droplet is falling (negative v). A falling droplet quickly reaches a constant speed, called the terminal speed. Write an expression for the terminal speed \(v_{term}\) in terms of m, g, and b. c. A spherical object of radius r moving slowly through the air is known to experience a retarding force \(F_{drag}= -6\pi \eta rv\) where \(\eta\) is the viscosity of the air. Use this and your answer to part b to show that a spherical droplet of density \(\rho\) falling with a terminal velocity \(v_{term}\) has a radius \(r=\sqrt{\frac{9 \eta v_{\text {term }}}{2 \rho g}}\) d. Oil has a density 860 \(kg/m^3\) . An oil droplet is suspended between two plates 1.0 cm apart by adjusting the potential difference between them to 1177 V. When the voltage is removed, the droplet falls and quickly reaches constant speed. It is timed with a stopwatch, and falls 3.00 mm in 7.33 s. The viscosity of air is \(1.83\times 10^{-5}\) kg/ms. What is the droplet’s charge? e. How many units of the fundamental electric charge does this droplet possess?

A classical atom orbiting at frequency f would emit electromagnetic waves of frequency f because the electrons orbit, seen edge-on, looks like an oscillating electric dipole. a. At what radius, in nm, would the electron orbiting the proton in a hydrogen atom emit light with a wavelength of 600 nm? b. What is the total mechanical energy of this atom?