Portions of electromagnetic waves A, B, and C are

Problem 3P In the mid-17th century, Isaac Newton proposed that light existed as a stream of particles, and the wave-particle debate continued for over 250 years until Planck and Einstein presented their revolutionary ideas. Give two pieces of evidence for the wave model and two for the particle model.

Problem 2P Consider the following types of electromagnetic radiation: (1) Microwave (2) Ultraviolet (3) Radio waves (4) Infrared (5) X-ray (6) Visible (a) Arrange them in order of increasing wavelength. ________________ (b) Arrange them in order of increasing frequency. ________________ (c) Arrange them in order of increasing energy.

Problem 1P In what ways are microwave and ultraviolet radiation the same? In what ways are they different?

Problem 5P What new idea about light did Einstein use to explain the photoelectric effect? Why does the photoelectric effect exhibit a threshold frequency? Why does it not of exhibit a time lag?

An AM station broadcasts rock music at \(^{\prime\prime}950\) on your radio dial.” Units for AM frequencies are given in kilohertz (kHz). Find the wavelength of the station’s radio waves in meters (m), nanometers (nm), and angstroms \((\overset{\circ} A)\). Equation Transcription: Å Transcription: ''950 Å

Portions of electromagnetic waves \(A\), \(B\), and \(C\) are represented below (not drawn to scale): Rank them in order of (a) increasing frequency; (b) increasing energy; (c) increasing amplitude. (d) If wave \(B\) just barely fails to cause a current when shining on a metal, is wave \(A\) or \(C\) more likely to do so? (e) If wave \(B\) represents visible radiation, is wave \(A\) or \(C\) more likely to be \(IR\) radiation? Equation Transcription: Text Transcription: A B C B A C B A C IR

An FM station broadcasts classical music at \(93.5 \ MHz\) (megahertz, or \(10^6\mathrm{\ Hz}\)). Find the wavelength (in m, nm, and \(\overset{\circ} A\)) of these radio waves. Equation Transcription: Å Text Transcription: 93.5 MHz 106 Hz Å

An x-ray has a wavelength of \(1.3 \ \overset{\circ} A\). Calculate the energy (in \(J\)) of one photon of this radiation. Equation Transcription: Å Text Transcription: 1.3 Å J

Problem 12P Rank the following photons in terms of decreasing energy: (a) IR (v = 6.5 × 1013 s?1); ________________ (b) microwave (v = 9.8 × 1011 s?1); ________________ (c) UV (v = 8.0 × 1015 s?1).

Problem 13P Cobalt-60 is a radioactive isotope used to treat cancers. A gamma ray emitted by this isotope has an energy of 1.33 MeV (million electron volts; 1 eV = 1.602 × 10?19 J). What is the frequency (in Hz) and the wavelength (in m) of this gamma ray?

(a) The first step in the formation of ozone in the upper atmosphere occurs when oxygen molecules absorb \(UV\) radiation of wavelengths \(\le242\mathrm{\ nm}\). Calculate the frequency and energy of the least energetic of these photons. (b) Ozone absorbs light having wavelengths of \(2200\) to \(2900 \ \overset{\circ} A\), thus protecting organisms on Earth’s surface from this high energy \(UV\) radiation. What are the frequency and energy of the most energetic of these photons? Equation Transcription: Å Text Transcription: UV leq 242 nm 2200 2900 Å UV

Problem 15P How is n1 in the Rydberg equation (Equation 7.3) related to the quantum number n in the Bohr model of the atom?

Problem 16P Distinguish between an absorption spectrum and an emission spectrum. With which did Bohr work?

Problem 11P Rank the following photons in terms of increasing energy: (a) blue (? = 453 nm); ________________ (b) red (? = 660 nm); ________________ (c) yellow (? = 595 nm).

Problem 17P Which of these electron transitions correspond to absorption of energy and which to emission? (a) n = 2 to n =4 ________________ (b) n = 3 to n = 1 ________________ (c) n = 5 to n = 2 ________________ (d) n = 3 to n = 4

Problem 19P Use the Rydberg equation (Equation 7.3) to calculate the wavelength (in nm) of the photon emitted when a hydrogen atom undergoes a transition from n = 5 to n = 2.

Problem 18P Why could the Bohr model not predict line spectra for atoms other than hydrogen?

Problem 22P Calculate the energy difference (?E) for the transition in Problem 7.24 for 1 mol of H atoms.

Problem 24P Arrange the following H atom electron transitions in order of decreasing wavelength of the photon absorbed or emitted: (a) n = 2 to n = ? ________________ (b) n = 4 to n = 20 ________________ (c) n = 3 to n = 10 ________________ (d) n = 2 to n = 1

Problem 27P In addition to continuous radiation, fluorescent lamps emit sharp lines in the visible region from a mercury discharge within the tube. Much of this light has a wavelength of 436 nm. What is the energy (in J) of one photon of this light?

Problem 21P Calculate the energy difference (?E) for the transition in Problem 7.23 for 1 mol of H atoms.

Problem 25P The electron in a ground-state H atom absorbs a photon of wavelength 97.20 nm. To what energy level does it move?

Problem 23P Arrange the following H atom electron transitions in order of increasing frequency of the photon absorbed or emitted: (a) n = 2 to n = 4 ________________ (b) n = 2 to n = 1 ________________ (c) n = 2 to n = 5 ________________ (d) n = 4 to n = 3

Problem 26P An electron in the n = 5 level of an H atom emits a photon of wavelength 1281 nm. To what energy level does it move?

A Bohr-model representation of the \(H\) atom is shown below with several electron transitions depicted by arrows: (a) Which transitions are absorptions and which are emissions? (b) Rank the emissions in terms of increasing energy. (c) Rank the absorptions in terms of increasing wavelength of light emitted. Equation Transcription: Text Transcription: H

Problem 29P If particles have wavelike motion, why don’t we observe that motion in the macroscopic world?

How fast must a \(142-\mathrm{g}\) baseball travel in order to have a de Broglie wavelength that is equal to that of an \(x\)-ray photon with \(\lambda=100 . \mathrm{pm}\)?

How fast must a \(56.5-g\) tennis ball travel in order to have a de Broglie wavelength that is equal to that of a photon of green light \((2900 \ \overset{\circ} A)\)? Equation Transcription: Å) Text Transcription: 56.5-g (5400 Å)

Problem 30P Why can’t we overcome the uncertainty predicted by Heisen- berg’s principle by building more precise devices to reduce the error in measurements below the h/4? limit?

Problem 36P A lithium flame has a characteristic red color due to emissions of wavelength 671 nm. What is the mass equivalence of 1 mol of photons of this wavelength (1 J = 1 kg·m2/s2)?

Problem 35P A sodium flame has a characteristic yellow color due to emissions of wavelength 589 nm. What is the mass equivalence of one photon of this wavelength (1J = 1 kg·m2/s2)?

Problem 37P What physical meaning is attributed to ?2, the square of the wave function?

Problem 39P What feature of an orbital is related to each of the following quantum numbers? (a) Principal quantum number (n) ________________ (b) Angular momentum quantum number (l) ________________ (c) Magnetic quantum number (ml)

Problem 38P What does “electron density in a particular tiny volume of space” mean?

Problem 41P How many orbitals in an atom can have each of the following designations: (a) 5f; ________________ (b) 4p; ________________ (c) 5d; ________________ (d) n = 2?

Problem 43P Give all possible ml values for orbitals that have each of the following: (a) l = 3; ________________ (b) n = 2; ________________ (c) n = 6, l = 1.

Problem 42P Give all possible ml values for orbitals that have each of the following: (a) l = 2; ________________ (b) n = 1; ________________ (c) n = 4, l = 3.

Problem 40P How many orbitals in an atom can have each of the following designations: (a) 1s; ________________ (b) 4d; ________________ (c) 3p; ________________ (d) n = 3?

Problem 46P For each of the following sublevels, give the n and l values and the number of orbitals: (a) 5s; (b) 3p; (c) 4f.

Problem 45P For each of the following, give the sublevel designation, the allowable ml values, and the number of orbitals: (a) n = 2, l = 0 ________________ (b) n = 3, l = 2 ________________ (c) n = 5, l = 1

Problem 44P For each of the following, Give the sublevel designation. The allowable ml values, and the number of orbitals: (a) n = 4, l = 2 ________________ (b) n = 5, l = 1 ________________ (c) n = 6, l = 3

Problem 48P Are the following quantum number combinations allowed? If not, show two ways to correct them : (a) n = 2; l = 0; ml = ?1 ________________ (b) n =4; l = 3; ml = ?1 ________________ (c) n = 3; l = 1; ml = 0 ________________ (d) n = 5; l = 2; ml = +3

Problem 49P Are the following quantum number combinations allowed? If not, show two ways to correct them: (a) n = 1; l = 0; ml = 0 ________________ (b) n = 2; l = 2; ml = +1 ________________ (c) n = 7; l = 1; ml = +2 ________________ (d) n = 3; l = 1; ml = ?2

Problem 47P For each of the following sublevels, give the n and l values and the number of orbitals: (a) 6g; ________________ (b) 4s; ________________ (c) 3d.

The photoelectric effect is illustrated in a plot of the kinetic energies of electrons ejected from the surface of potassium metal or silver metal at different frequencies of incident light. (a) Why don’t the lines begin at the origin? (b) Why don’t the lines begin at the same point? (c) From which metal will light of a shorter wavelength eject an electron? (d) Why are the slopes of the lines equal?

Problem 51P The human eye is a complex sensing device for visible light. The optic nerve needs a minimum of 2.0 × 10-17 J of energy to trigger a series of impulses that eventually reach the brain. (a) How many photons of red light (700. nm) are needed? ________________ (b) How many photons of blue light (475 nm)?

Problem 55P In his explanation of the threshold frequency in the photoelectric effect, Einstein reasoned that the absorbed photon must have a minimum energy to dislodge an electron from the metal surface. This energy is called thework function (?) of that metal. What is the longest wavelength of radiation (in nm) that could cause the photoelectric effect in each of these metals: (a) calcium, ? = 4.60 × 10-19 J ; (b) titanium, ? = 6.94 × 10?19 J; (c) sodium, ? = 4.41 × 10?19 J?

One reason carbon monoxide (CO) is toxic is that it binds to the blood protein hemoglobin more strongly than oxygen does. The bond between hemoglobin and \(\mathrm{CO}\) absorbs radiation of \(1953 \mathrm{~cm}^{-1}\). (The units are the reciprocal of the wavelength in centimeters.) Calculate the wavelength (in \(\mathrm{nm}\) and \(\AA\) ) and the frequency (in \(\mathrm{Hz}\) ) of the absorbed radiation. Equation Transcription: Text Transcription: CO 1953 cm^?1 nm AA Hz

Problem 57P A laser (light amplification by stimulated emission of radiation) provides a coherent (in-phase) nearly monochromatic source of high-intensity light. Lasers are used in eye surgery, CD/DVD players, basic research, etc. Some modern dye lasers can be "tuned" to emit a desired wavelength. Fill in the blanks in the following table of the properties of some common lasers: Type ? (nm) v (s-1) E(J) Color He-Ne 632.8 ? ? ? Ar ? 6.148 × 1014 ? ? Ar-Kr ? ? 3.499 × 10-19 ? Dye 663.7 ? ? 7

Problem 54P TV and radio stations transmit in specific frequency bands of the radio region of the electromagnetic spectrum. (a) TV channels 2 to 13 (VHF) broadcast signals between the frequencies of 59.5 and 215.8 MHz, whereas FM radio stations broadcast signals with wavelengths between 2.78 and 3.41 m. Do these bands of signals overlap? ________________ (b) AM radio signals have frequencies between 550 and 1600 kHz. Which has a broader transmission band, AM or FM?

Problem 53P A metal ion Mn+ has a single electron. The highest energy line in its emission spectrum occurs at a frequency of 2.961 × 1016 Hz. Identify the ion.

Problem 56P You have three metal samples—A, B, and C—that are tantalum (Ta), barium (Ba), and tungsten (W), but you don't know which is which. Metal A emits electrons in response to visible light; metals B and C require UV light, (a) Identify metal A, and find the longest wavelength that removes an electron, (b) What range of wavelengths would distinguish B and C? [The work functions are Ta (6.81 × 10?19 J), Ba (4.30 × 10?19 J), and W (7.16 × 10?19 J); work function is explained in Problem 7.70.]

Problem 58P As space exploration increases, means of communication with humans and probes on other planets are being developed. (a) How much time (in s) does it take for a radio wave of frequency 8.93 × 107 s-1 to reach Mars, which is 8.1 × 107 km from Earth? (b) If it takes this radiation 1.2 s to reach the Moon, how far(in m) is the Moon from Earth?

Use the relative size of the \(3 s\) orbital represented on the next page to answer the following questions about orbitals A–D. (a) Which orbital has the highest value of \(n\) ? (b) Which orbital(s) have a value of \(l=1 ? l=2\) ? (c) How many other orbitals with the same value of \(n\) have the same shape as orbital B? Orbital C? (d) Which orbital has the highest energy? Lowest energy? Equation Transcription: Text Transcription: 3s n |=1 |=2

Photoelectron spectroscopy applies the principle of the photoelectric effect to study orbital energies of atoms and molecules. High-energy radiation (usually UV or x-ray) is absorbed by a sample and an electron is ejected. By knowing the energy of the radiation and measuring the energy of the electron lost, the orbital energy can be calculated. The following energy differences were determined for several electron transitions: \(\Delta E_{2 \longrightarrow 1}=4.098 \times 10^{-17} \mathrm{~J}\) \(\Delta E_{3 \longrightarrow 1}=4.854 \times 10^{-17} \mathrm{~J}\) \(\Delta E_{5 \longrightarrow 1}=5.242 \times 10^{-17} \mathrm{~J}\) \(\Delta E_{4 \longrightarrow 2}=1.024 \times 10^{-17} \mathrm{~J}\) Calculate the energy change and the wavelength of a photon emitted in the following transitions. (a) Level \(3 \longrightarrow 2\) (b) Level \(4 \longrightarrow 1\) (c) Level \(5 \longrightarrow 4\) Equation Transcription: Text Transcription: DeltaE_2 longrightarrow 1 =4.098 x 10^?17 J Delta E_3 longrightarrow 1 =4.854x10^?17 J Delta E_5 longrightarrow 1 =5.242 x 10^?17 J Delta E_4 longrightarrow 2=1.024x10^?17 J 3 longrightarrow 2 4 longrightarrow 1 5 longrightarrow 4

The quantum-mechanical treatment of the hydrogen atom gives an expression for the wave function, \(\Psi\), of the 1s orbital: \(\psi=\frac{1}{\sqrt{\pi}}\left(\frac{1}{a_{0}}\right)^{3 / 2} e^{-r / a_{0}}\) where r is the distance from the nucleus and a0 is \(52.92 pm\). The electron probability density is the probability of finding the electron in a tiny volume at distance r from the nucleus and is proportional to \(\Psi^{2}\). The radial probability distribution is the total probability of finding the electron at all points at distance r from the nucleus and is proportional to 4????r2?2. Calculate the values (to three significant figures) of \(\Psi\), \(\Psi^{2}\), and \(4 \pi r^{2} \Psi^{2}\) to fill in the following table, and sketch plots of these quantities versus r. Compare the latter two plots with those in Figure 7.16A: Equation Transcription: ? ?2 Text Transcription: Psi Psi=1/sqrt pi (1/a_0)^3/2 e^-r/a_0 52.92 pm Psi^2 4 pi r^2 \Psi^2

Problem 59P A ground-state H atom absorbs a photon of wavelength 94.91 nm, and its electron attains a higher energy level. The atom then emits two photons: one of wavelength 1281 nm to reach an intermediate level, and a second to reach the ground state. (a) What higher level did the electron reach? ________________ (b) What intermediate level did the electron reach? ________________ (c) What was the wavelength of the second photon emitted?

Problem 62P Enormous numbers of microwave photons are needed to warm macroscopic samples of matter. A portion of soup containing 252 g of water is heated in a microwave oven from 20.°C to 98°C, with radiation of wavelength 1.55 × 10?2 m. How many photons are absorbed by the water in the soup?

Problem 65P An electron microscope focuses electrons through magnetic lenses to observe objects at higher magnification than is possible with a light microscope. For any microscope, the smallest object that can be observed is one-half the wavelength of the radiation used. Thus, for example, the smallest object that can be observed with light of 400 nm is 2 × 10?7 m. (a) What is the smallest object observable with an electron microscope using electrons moving at 5.5 × 104 m/s? (b) At 3.0 × 107 m/s?

Problem 66P In a typical fireworks device, the heat of the reaction between a strong oxidizing agent, such as KC104, and an organic compound excites certain salts, which emit specific colors. Strontium salts have an intense emission at 641 nm, and barium salts have one at 493 nm. (a) What colors do these emissions produce? (b) What is the energy (in kJ) of these emissions for 5.00 g each of the chloride salts of Sr and Ba? (Assume that all the heat released is converted to light emitted.)

Problem 68P Fish-liver oil is a good source of vitamin A, which is measured spectrophotometrically, after correcting for background, at a wavelength of 329 nm. (a) Suggest a reason for using this wavelength. ________________ (b) In what region of the spectrum does this wavelength lie? ________________ (c) When 0.1232 g of fish-liver oil is dissolved in 500. mL of solvent, the absorbance is 0.724 units. When 1.67 × 10?3 g of vitamin A is dissolved in 250. mL of solvent, the absorbance is 1.018 units. Calculate the vitamin A concentration in the fish-liver oil.

Problem 67P Atomic hydrogen produces well-known series of spectral lines in several regions of the electromagnetic spectrum. Each series fits the Rydberg equation with its own particular n1 value. Calculate the value of n1 (by trial and error if necessary) that would produce a series of lines in which: (a) The highest energy line has a wavelength of 3282 nm. ________________ (b) The lowest energy line has a wavelength of 7460 nm.

Problem 70P In a game of “Clue,” Ms. White is killed in the conservatory. You have a device in each room to help you find the murderer a spectrometer that emits the entire visible spectrum to indicate who is in that room. For example, if someone wearing yellow is in a room, light at 580 nm is reflected. The suspects are Col. Mustard, Prof. Plum, Mr. Green, Ms. Peacock (blue), and Ms. Scarlet. At the time of the murder, the spectrometer in the dining room recorded a reflection at 520 nm, those in the lounge and study recorded reflections of lower frequencies, and the one in the library recorded a reflection of the shortest possible wavelength. Who killed Ms. White? Explain.

Technetium (\(Tc; Z = 43\)) is a synthetic element used as a radioactive tracer in medical studies. ATc atom emits a beta particle (electron) with a kinetic energy (\(E_{k}\)) of \(4.71 \times 10^{-15} \mathrm{~J}\). What is the de Broglie wavelength of this electron (\(\mathrm{E}_{\mathrm{k}}=\frac{1}{2} m v^{2}\))? Equation Transcription: Ek 4.71x10-15 J Ek = Text Transcription: Tc; Z = 43 E_k 4.71x10^-15 J E_k = 1/2mv^2

Problem 73P The net change in the multistep biochemical process of photosynthesis is that CO2 and H2O form glucose (C6H12O6) and O2. Chlorophyll absorbs light in the 600 to 700 nm region, (a) Write a balanced thermochemical equation for formation of 1.00 mol of glucose, (b) What is the minimum number of photons with ? = 680. nm needed to prepare 1.00 mol of glucose?

Problem 69P Many calculators use photocells to provide their energy. Find the maximum wavelength needed to remove an electron from silver (? = 7.59 × 10?19 J). Is silver a good choice for a photocell that uses visible light?

Problem 72P Electric power is typically given in units of watts (1 W = 1 J/s). About 95% of the power output of an incandescent bulb is converted to heat and 5% to light. If 10% of that light shines on your chemistry text, how many photons per second shine on the book from a 75-W bulb? (Assume the photons have a wavelength of 550 nm.)

Problem 20P Use the Rydberg equation to calculate the wavelength in (Å) of the photon absorbed when a hydrogen atom undergoes a transition from n = 1 to n = 3.