Solved: A neon discharge emits a bright reddish-orange

A neon discharge emits a bright reddish-orange spectrum. But a glass tube filled with neon is completely transparent. Why doesn' t the neon in the tube absorb orange and red wavelengths?

The two spectra shown in Figure Q29.2 belong to the same element, a fictional Element X. Explain why they are different.

Is a spectral line with wavelength 6S6 nm seen in the absorption spectrum of hydrogen atoms? Why or why not?

Can nuclei of the same element have different values of Z? Of N? Of A? Can nuclei of different elements have the same values of Z? Of N? Of A?

An atom has four energy levels. How many spectral lines are seen in its emission spectrum? In its absorption spectrum? How many absorption lines?

If an electron is in a stationary state of an atom, is the electron at rest? If not, what does the term mean?

The n = 3 state of hydrogen has 3 = - l.S l e V. a. Why is the energy negative? b. What is the physical significance of the specific number l.S l eV?

For a hydrogen atom, list all possible states (11, /, m, m, ) that have = - I.SI eY.

What are then and l values of the following states ofa hydrogen atom: (a) 4d, (b) Sf, (c) 6s?

How would you label the hydrogen-atom states with the fol lowing (11, /, 111) quantum numbers: (a) (4, 3, 0), (b) (3, 2, I), (c) (3, 2, - 1)?

A hydrogen atom is in a state with pri ncipal quantum number 11 = S. What possible values of the orbital quantum number I could this atom have?

Consider the two hydrogen-atom states Sd and 4f Which has the higher energy? Explain.

In a multielectron atom, does a Ss electron have higher or lower energy than a 4f electron? Explain.

Do the following electron configurations represent a possible state of an element? If so, (i) identify the element and (ii) determine if this is the ground state or an excited state. If not, why not? a. I s22s22p63s2 b. I s22s22p73s c. b :i2s22p43s23p2

Why is the section of the periodic table labeled as "transition elements" exactly 10 elements wide in all rows?

An electron is in an f state. Can it undergo a quantum jump to an s state? A p state? Ad state? Explain.

Figure Q29. I 7 shows the energy-level diagram of Element X. a. What is the ionization energy of Element X? b. An atom in the ground state absorbs a photon, then emits a photon with a wavelength of 1240 nm. What conclusion can you draw about the energy of the photon that was absorbed? c. An atom in the ground state has a collision with an electron , then emits a photon with a wavelength of 1240 nm. What conclusion can you draw about the initial kinetic energy of the electron?

a. Which states of a hydrogen atom can be excited by a colli sion with an electron with kinetic energy K = 12.S eV? Explain. b. After the collision the atom is not in its ground state. What happens to the electron? (i) Tt bounces off with K > 12.S eY, (ii) It bounces off with K = 12.S e V, (iii) It bounces off with K < 12.S eV, (iv) It is absorbed by the atom. Explain your choice. c. After the collision, the atom emits a photon. List all the possible 11--> /11 transitions that might occur as a result of this collision.

What is an atom's ioni zation energy? In other words, if you know the ionization energy of an atom, what is it that you know about the atom?

Figure Q29.20 shows the energy levels of a hypothetical atom. a. What minimum kinetic energy (in e V) must an electron have to colli sionally excite this atom and cause the emission of a 620 nm photon? Explain. b. Can an electron with K = 6 e V cause the emission of 620 nm light? lf so, what is the final kinetic energy of the FIGURE 02920 electron? If not, why not? c. Can a 6 eV photon cause the emission of 620 nm light from this atom? Why or why not? d. Can a 7 e V photon cause the emission of 620 nm I ight from this atom? Why or why not?

Seven possible transitions are identified on the energy-level diagram in Figure Q29.2 I. For each, is this an allowed transition? If allowed, is it an emission or an absorption transition, and is the photon infrared, visible, or ultraviolet? If not allowed, why not?

A 2.0 eV photon is incide nt on an atom in the p state, as shown in the energy-level diagram in Figure Q29.22. Does the atom undergo an absorption transition, a stimulated emission transition, or neither? Explain.

A glass tube contains 2 X !011 atoms, some of which are in the ground state and some of which are excited. Figure Q29.23 shows the populations for the atoms' three energy levels. ls it possible for these atoms to be a laser? If so, on which transition would laser action occur? If not, why not?

An e lectron collides with an atom in its ground state. The atom then emits a photon of energy Ephoion In this process the change D.E0 10c in the electron's energy is A. Greater than Ephoion. B. Greater than or equal to Ephoion C. Equal to Ephoion D. Less than or equal to photon E. Less than photon.

How many states are in the I = 4 subshell? A. 8 B. 9 C. 16 D. 18 E . 22

What is the ground-state electron configuration of calcium (Z = 20)? A. I s22s22p63s23p8 B. ls22s22p63s23p64s14p1 C. I s22s22p63s23p64s2 D. ls225221hs23p64p2

An atom emits a photon with a wavelength of 275 nm. By how much does the atom's energy change? A. 0.72 eV B. 1.06 eV C. 2.29 eV D. 3.06eV E. 4.5 1 eV

The energy of a hydrogen atom is -3.40 eV. What is the electron' s kinetic energy? A. 1.70 eV B. 2.62 eV C. 3.40 eV D. 5.73 eV E. 6.80 eV

The angular momel)tum of an electron in a Bohr hydrogen atom is 3. 18 x I0- 34 kg m2 /s. What is the atom's energy? A. -13.60eV B. - 6.73eV C. - 3.40eV D. -I.51 eV E. - 0.47 eV

A "soft x-ray" photon with an energy of 4 1.8 e V is absorbed by a hydrogen atom in its ground state, knocking the atom's electron out. What is the speed of the e lectron as it leaves the atom? A. 1.84 X 105 m/s B. 3.08 X 105 m/s C. 8.16 X !05 m/s D. 3. 15 x 106 mis E. 3.83 x I 06 mis

Explain what is wrong with these e lectron configurations: a. Is22s22p83s23p* b. ls22s32p4

Which has higher energy: an electron in the 4f state or an electron in the 7s state? Explain.

An electron with a speed of S.00 X I 06 mis collides with an atom. The collision excites the atom from its ground state (0 e V) to a state with an energy of 3.80 eY. What is the speed of the electron after the collision?

Hydrogen gas absorbs light of wavelength 103 nm. Afterward, what wavelengths are seen in the emission spectrum?

What is the longest wavelength of light that can excite the 4s stale of sodium?

An electron with a kinetic e nergy of 3.90 eY collides with a sodium atom. What possible wavele ngths of light are subsequently emitted?

a. Is a 4p -+ 4s transition allowed in sodium? If so, what is its wavelength? lf not, why not? b. Is a 3d--+ 4s transiti on allowed in sodium? If so, what is its wavelength? If not, why not?

Figure P29.38 shows a molecular energy-le vel diagram. What are the longest and shortest wavele ngths in (a) the molecule's absorption spectrum and (b) the molec ule's fluorescence specuum?

The molecule whose energy-level diagram is shown in Figure P29.38 is illuminated by 2.7 eV photons. What is the longest wavelength of light that the molecule can emit?

A 1000 W carbon dioxide laser emits an infrared laser beam with a wavelength of 10.6 ,m. How many photons are emitted per second?

A 1.00 mW helium-neon laser emits a visible laser beam with a wavelength of 633 nm. How many photons are emitted per second?

In LASIK surgery, a laser is used to reshape the cornea of BIO the eye to improve vision. The laser produces extremely short INT pulses of light, each containing 1.0 mJ of energy. a. In each pulse there are 9.7 x !014 photons. What is the wavelength of the laser? b. Each pulse lasts only 20 ns. What is the average. power delivered to the eye during a pulse?

A ruby laser emits an intense pulse of light that lasts a mere 10 ns. The light has a wavelength of 690 nm, and each pulse has an energy of 500 mJ. a. How many photons are emitted in each pulse? b. What is the ra/e of photon emission, in photons per second, during the I 0 ns that the laser is "on"?

A 2.55 eY photon is emitted from a hydrogen atom. What are the Balmer formula n and m values corresponding to this emission?

Two of the wavelengths emitted by a hydrogen atom are 102.6 nm and 1876 nm. a. What are the Balmer formula n and /11 values for each of these wavelengths? b. For each of these wavelengths, is the light infrared, visible, or ultraviolet?

In Example 29.2 it was assumed that the initially stationary gold nucleus would remain motionless during a head-on collision with an 8.3 MeY alpha parti cle. What is the actual recoil speed of the gold nucleus after that elastic collision? Assume that the mass of a gold nucleus is exactly 50 times the mass of an alpha particle. Hint: Review the discussion of perfectly elastic collisions in Chapter 10.

Consider the gold isotope 197 Au. a. How many electrons, protons, and neutrons are in a neutral 197Au 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 207Pb. a. How many electrons, protons, and neutrons are in a neutral 207Pb atom? b. The lead nucleus has a diameter of 14.2 fm. What are the electric potential and the electric field strength at the surface of a lead nucleus?

The diameter of an atom is 1.2 X 10- 10 m and the diameter of its nuc leus is 1.0 X I0- 14 m. What percent of the atom's volume is occupied by mass and what percent is empty space?

The charge-to-mass ratio of a nucleus, in units of elu, is q/111 =ZIA. For example, a hydrogen nucleus has q/m = 1/1 = I. a. Make a graph of charge-to-mass ratio versus proton number Z for nuclei with Z = 5, 10, 15, 20, ... , 90. For A, use the average atomic mass shown on the periodic table of elements in Appendix B. Show each of these 18 nuclei as a dot, but don't connect the dots together as a c urve. b. Describe any trend that you notice in your graph. c. What's happening in the nuclei that is responsible for this trend?

If the nucleus is a few fm in diameter, the distance between the centers of two protons must be = 2 fm. a. Calculate the repulsive electric force between two protons that are 2.0 fm apart. b. Calculate the attractive gravitational force be tween two protons that are 2.0 fm apart. Could gravity be the force that holds the nucleus together?

In a head-on collision, the closest approach of a 6.24 MeY alpha particle to the center of a nucleus is 6.00 fm. The nucleus is in an atom of what element? Assume that the nucleus is heavy enough to remain stationary during the collision.

A 20 MeV alpha particle is fired toward a 238U nucleus. It fo llows the path shown in Figure P29.53. What is the alpha particle's speed when it 20 fm is closest to the nucleus, 20 fm from its center? Assume that the nucleus doesn't move.

The oxygen nucleus 160 has a radius of 3.0 fm. INT 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 that the nucleus is heavy enough ro remain stationary during the collision. b. What is the proton's kinetic energy in MeY?

The absorption spectrum of an atom consists of the wavelengths 200 nm, 300 nm, and 500 nm. a. Draw the atom's energy-level diagram. b. What wavelengths are seen in the atom's emission spectrum?

The first three energy levels of the fictitious element X are shown in Figure P29.56. a. What wavelengths are observed in the absorption spectrum of element X?Give your answers in nm.State whether each of your wavelengths in part a corcorresponds to ultraviolet, visible, or infrared light. c. An electron with a speed of 1.4 X I 06 mis collides with an atom of element X. Shmtly afterward, the atom emits a 1240 nm photon. What was the electron's speed after the colli sion? Assume that, because the atom is so much more massive than the electron, the recoil of the atom is negligible.

A simple atom has four lines in its absorption spectrum. Ignoring any selection rules, how many lines will it have in its emission spectrum?

A simple atom has only two absorption lines, at 250 nm and 600 nm. What is the wavele ngth of the one line in the emission spectrum that does not appear in the absorption spectrum?

What is the wavelength of the series limit ( i.e., the shortest possible wavelength) of the Lyman series in hydrogen?

What is the energy of a Bohr hydrogen atom with a 5.18 nm diameter?

A hydrogen atom in the ground state absorbs a 12.75 eY photo n. Immediately after the absorption, the atom undergoes a quantum jump to the next-lowest energy level. What is the wavelength of the photon emitted in this quantum jump?

Potassium atom I, with a mass of 6.47 x I 0- 26 kg, has a speed of 1.30 X I 04 mis. It collides with potassium atom 2 that is at rest, exciting atom 2 to a state from which it emits a 3.06 eY photon as it returns to the ground state. Atom 2 leaves the collision with a speed of 1.17 x I 04 mis. What is the final speed of atom I?

a. Calculate the orbital radius and the speed of an electron in \both the 11 = 99 and the 11 = I 00 s tates of hydrogen. b. Determine the orbital frequency of the electron in each of these states. c. Calculate the frequency of a photon emiued in a 100-+ 99 transition. d. Compare the photon frequency of part c to the average of your two orbital freq uencies from part b. By what percent do they differ?

Two hydrogen atoms collide head-on. The coll ision brings both atoms to a halt. Immediately after the collision, both atoms emit a 121.6 nm photon. What was the speed of each atom just before the collision?

A beam of electrons is incident on a gas of hydrogen atoms. a. What minimum speed must the e lectrons have to cause the emission of 656 nm light from the 3 -+ 2 transition of hydrogen? b. Through what potential difference must the electrons be accelerated to have this speed?

A hydrogen atom in its fourth excited state emits a photon with a wavele ngth of 1282 nm. What is the atom's maximum possible orbital angular momentum after the emission? Give your answer as a multiple of h.

A particular emission line in the hydrogen spectrum has a wavelength of 656.5 nm. What are all possible trans itions (e .g., &/-+ 2s) that could give rise to this emission?

Germicidal lamps are used to sterilize tools in biological and medical fac ilities. One type of germicidal lamp is a low pressure mercury discharge tube, simi lar to a nuorescent lightbulb, that has been optimized to emit ultraviolet light with a wavelength of 254 nm. A 15-mm-diameter, 25-cm-long tube emits 4.5 W of ultraviolet light. The mercury vapor pressure ins ide the tube is 1.0 Pa at the operating temperature of 40C. a. On average, how many ultraviolet photons does each mercury atom emit per second? b. The lifetime of the excited state in mercury is a rather long 120 ns. On average, what fraction of its time does a mercury atom spend in the excited state?

a. What downward transitions are possible for a sodium atom in the 6s s tate? (See Figure 29.24.) b. What are the wavelengths of the photons emiued in each of these transitions?

The Sd ~ 3p transition in the emission spectrum of sodi um (see Figure 29.24) has a wavelength of 499 nm. What is the energy of the Sd state?

A sodium atom (see Figure 29.28) in the 3p state emits a photon, decreas ing the energy of the atom by 2.10 e V. By how much does the orbital angular momentum of the atom change? Does it increase or decrease?

Figure P29.72 shows a few energy leve ls of the mercury atom. One valence electron is always in the 6s s tate; the other electron changes states. a . Make a table showing all the allowed transitions in the emission spectrum. For each transition, indicate the photon wavelength, in nm. b. What minimum speed must an electron have to excite the 492-nm-wavelength blue emission line in the Hg spectrum?

A laser emits 1.00 X 1019 photons per second from an exINT cited state with energy 2 = l. 17 e V. The lower energy level is 1 =OeV. a. What is the wavelength of this laser? b. What is the power output of this laser?

Fluorescence microscopy, discussed in Section 29.8, is an important tool in modern cell biology. A variation on this techINT nique depends on a phenomenon known as two-photon excitation. If two photons are absorbed simultaneously (i.e., within about w- 16 s), their energies can add. A molecule that is normally excited by a 350 nm photon can be excited by two photons each having half as much energy. For this process to be useful, photons must illuminate Lhe sample at the very high rate of at least I 029 photons/m2 s. This is achieved by focusing a laser beam to a small spot and by concentrating the power of the laser into very short (10- 13 s) pulses that are fired 108 times each second. Suppose a biologist wants to use two-photon excitation to excite a molecular species that would be excited by 500 nm light in normal one-photon fluorescence microscopy. What minimum intensity (W/m2 ) must the laser beam have during each pulse?

An LED emits green light. Increasing the size of the band gap could change the color of the emitted light to A. Red B. Orange C. Yellow D. Blue

Suppose the LED band gap is 2.S eV, which corresponds to a wavelength of SOO nm. Consider the possible electron transitions in Figure P29.76. SOO nm is the A. Maximum wavelength of the LED. B. Average wavelength of the LED. C. Minimum wavelength of the LED.

The same kind of semiconducting materia l used to make an LED can also be used to convert absorbed light into electrical energy, essentially operating as an LED in reverse. In this case, the absorption of a photon causes an electron transition from a filled state in the valence band to an unfilled state in the conduction band. If t1000d = 1.4 eV, what is the minimum wavelength of electromagnetic radiation that could lead to electric energy output? A. 140 nm B. 890 nm C. 1400 nm D. 8900 nm

The efficiency of a light source is the percentage of its energy input that gets radiated as visible light. If some of the blue light in an LED is used to cause a fluorescent material to glow, A. The overall efficiency of tbe LEb is increased. B. The overall efficiency of the LED does n ot change. C. The overall efficiency of the LED decreases.