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Problem 63
Sketch the 1s and 2p orbitals. How do the 2s and 3p orbitals differ from the 1s and 2p orbitals?
Problem 64
Sketch the 3d orbitals. How do the 4d orbitals differ from the 3d orbitals?
- An electron in a hydrogen atom is excited with electrical energy to an excited state with n = 2. The atom then emits a photon. What is the value of n for the electron after the emission?
Problem 65
Problem 66
Determine whether each transition in the hydrogen atom corresponds to absorption or emission of energy. a. n = 3 → n = 1 b. n = 2 → n = 4 c. n = 4 → n = 3
- According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with the longer wavelength: 2p to 1s or 3p to 1s?
Problem 67
Problem 68
According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with the longer wavelength: 3p → 2s or 4p → 3p?
Problem 69
Calculate the wavelength of the light emitted when an electron in a hydrogen atom makes each transition and indicate the region of the electromagnetic spectrum (infrared, visible, ultraviolet, etc.) where the light is found. a. n = 2 → n = 1 b. n = 3 → n = 1 c. n = 4 → n = 2 d. n = 5 → n = 2
Problem 70
Calculate the frequency of the light emitted when an electron in a hydrogen atom makes each transition: a. n = 4 → n = 3 b. n = 5 → n = 1 c. n = 5 → n = 4 d. n = 6 → n = 5
Problem 71
An electron in the n = 7 level of the hydrogen atom relaxes to a lower-energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?
Problem 72
An electron in a hydrogen atom relaxes to the n = 4 level, emitting light of 114 THz. What is the value of n for the level in which the electron originated?
Problem 73
Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because these kinds of radiation carry enough energy to break bonds within the molecules. A typical carbon–carbon bond requires 348 kJ/mol to break. What is the longest wavelength of radiation with enough energy to break carbon–carbon bonds?
Problem 74
The human eye contains a molecule called 11-cis-retinal that changes shape when struck with light of sufficient energy. The change in shape triggers a series of events that results in an electrical signal being sent to the brain that results in vision. The minimum energy required to change the conformation of 11-cis-retinal within the eye is about 164 kJ/mol. Calculate the longest wavelength visible to the human eye.
Problem 75
An argon ion laser puts out 5.0 W of continuous power at a wavelength of 532 nm. The diameter of the laser beam is 5.5 mm. If the laser is pointed toward a pinhole with a diameter of 1.2 mm, how many photons travel through the pinhole per second? Assume that the light intensity is equally distributed throughout the entire cross-sectional area of the beam. (1 W = 1 J/s)
- A green leaf has a surface area of 2.50 cm². If solar radiation is 1000 W/m², how many photons strike the leaf every second? Assume three significant figures and an average wavelength of 504 nm for solar radiation.
Problem 76
- In a technique used for surface analysis called Auger electron spectroscopy (AES), electrons are accelerated toward a metal surface. These electrons cause the emissions of secondary electrons—called Auger electrons—from the metal surface. The kinetic energy of the Auger electrons depends on the composition of the surface. The presence of oxygen atoms on the surface results in Auger electrons with a kinetic energy of approximately 506 eV. What is the de Broglie wavelength of one of these electrons? [KE = 1/2mv^2; 1 electron volt (eV) = 1.602 * 10^(-19) J]
Problem 77
Problem 78
An X-ray photon of wavelength 0.989 nm strikes a surface. The emitted electron has a kinetic energy of 969 eV. What is the binding energy of the electron in kJ/mol? [KE = 1/2 mv2; 1 electron volt (eV) = 1.602×10–19 J]
Problem 79
Ionization involves completely removing an electron from an atom. How much energy is required to ionize a hydrogen atom in its ground (or lowest energy) state? What wavelength of light contains enough energy in a single photon to ionize a hydrogen atom?
Problem 80
The energy required to ionize sodium is 496 kJ/mol. What minimum frequency of light is required to ionize sodium?
Problem 81
Suppose that in an alternate universe, the possible values of l are the integer values from 0 to n (instead of 0 to n - 1). Assuming no other differences between this imaginary universe and ours, how many orbitals would exist in each level? a. n = 1 b. n = 2 c. n = 3
Problem 82
Suppose that, in an alternate universe, the possible values of ml are the integer values including 0 ranging from -l -1 to l +1 (instead of simply -l to +l). How many orbitals exist in each sublevel? a. s sublevel b. p sublevel c. d sublevel
Problem 83
An atomic emission spectrum of hydrogen shows three wavelengths: 1875 nm, 1282 nm, and 1093 nm. Assign these wavelengths to transitions in the hydrogen atom.
Problem 84
An atomic emission spectrum of hydrogen shows three wavelengths: 121.5 nm, 102.6 nm, and 97.23 nm. Assign these wavelengths to transitions in the hydrogen atom.
- The binding energy of electrons in a metal is 193 kJ/mol. What is the threshold frequency of the metal?
Problem 85
- In order for a thermonuclear fusion reaction of two deuterons (2^1H^+) to take place, the deuterons must collide and each must have a velocity of about 1 * 10^6 m/s. Find the wavelength of such a deuteron.
Problem 86
Problem 87
The speed of sound in air is 344 m/s at room temperature. The lowest frequency of a large organ pipe is 30 s–1 and the highest frequency of a piccolo is 1.5×104 s–1. Find the difference in wavelength between these two sounds.
Problem 88
The distance from Earth to the sun is 1.5×108 km. Find the number of crests in a light wave of frequency 1.0×1014 s –1 traveling from the sun to Earth.
Problem 90
A 5.00-mL ampule of a 0.100-M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 15.5 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?
Problem 91
A laser produces 20.0 mW of red light. In 1.00 hr, the laser emits 2.29×1020 photons. What is the wavelength of the laser?
Problem 92
A particular laser consumes 150.0 watts of electrical power and produces a stream of 1.33×1019 1064-nm photons per second. What is the percent efficiency of the laser in converting electrical power to light?
- Assuming total absorption of the light by the sample, what is the maximum amount (in moles) of CH3X that breaks apart when a cuvette containing a solution of CH3X is irradiated with 280-nm light with a power of 885 mW for 10.0 minutes, given that the quantum yield for the reaction CH3X → CH3 + X is f = 0.24?
Problem 93