Problem 28
An AM radio station broadcasts at 1010 kHz, and its FM partner broadcasts at 98.3 MHz. Calculate and compare the energy of the photons emitted by these two radio stations.
Problem 29c
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (c) How many photons are in a 1.00 mJ burst of this radiation?
Problem 29d
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (d) These UV photons can break chemical bonds in your skin to cause sunburn—a form of radiation damage. If the 325-nm radiation provides exactly the energy to break an average chemical bond in the skin, estimate the average energy of these bonds in kJ/mol.
Problem 30
The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of 242 kJ/mol is required to break the chlorine–chlorine bond in Cl2. What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?
Problem 31
A diode laser emits at a wavelength of 987 nm. (a) In what portion of the electromagnetic spectrum is this radiation found? (b) All of its output energy is absorbed in a detector that measures a total energy of 0.52 J over a period of 32 s. How many photons per second are being emitted by the laser?
Problem 32
A stellar object is emitting radiation at 3.55 mm. a. What type of electromagnetic spectrum is this radiation? b. If a detector is capturing 3.2×108 photons per second at this wavelength, what is the total energy of the photons detected in 1.0 hour?
Problem 33a
Molybdenum metal must absorb radiation with a minimum frequency of 1.09 * 1015 s - 1 before it can eject an electron from its surface via the photoelectric effect. (a) What is the minimum energy needed to eject an electron?
Problem 33b
Molybdenum metal must absorb radiation with a minimum frequency of 1.09 * 1015 s - 1 before it can eject an electron from its surface via the photoelectric effect. (b) What wavelength of radiation will provide a photon of this energy?
Problem 33c
Molybdenum metal must absorb radiation with a minimum frequency of 1.09 * 1015 s - 1 before it can eject an electron from its surface via the photoelectric effect. (c) If molybdenum is irradiated with light of wavelength of 120 nm, what is the maximum possible kinetic energy of the emitted electrons?
- Titanium metal requires light with a maximum wavelength of 286 nm to emit electrons. (a) What is the minimum energy of the photons necessary to emit electrons from titanium via the photoelectric effect? (b) If titanium is irradiated with light of wavelength 276 nm, what is the maximum possible kinetic energy of the emitted electrons?
Problem 34
Problem 35
Does the hydrogen atom 'expand' or 'contract' when an electron is excited from the n = 1 state to the n = 3 state?
Problem 36
Classify each of the following statements as either true or false: (a) A hydrogen atom in the n = 3 state can emit light at only two specific wavelengths (b) a hydrogen atom in the n = 2 state is at a lower energy than one in the n = 1 state (c) the energy of an emitted photon equals the energy difference of the two states involved in the emission.
Problem 37a
Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? a. from n = 4 to n = 2
Problem 37b
Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? b. from an orbit of radius 2.12 Å to one of radius 8.46 Å
Problem 38a
Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen: a. from n = 3 to n = 6
Problem 39a
a. Using Equation 6.5, calculate the energy of an electron in the hydrogen atom when n = 2 and when n = 6. Calculate the wavelength of the radiation released when an electron moves from n = 6 to n = 2.
Problem 40b2
Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. b. Will the light be absorbed or emitted?
Problem 41a
The visible emission lines observed by Balmer all involved nf = 2. (a) Which of the following is the best explanation of why the lines with nf = 3 are not observed in the visible portion of the spectrum: (i) Transitions to nf = 3 are not allowed to happen, (ii) transitions to nf = 3 emit photons in the infrared portion of the spectrum, (iii) transitions to nf = 3 emit photons in the ultraviolet portion of the spectrum, or (iv) transitions to nf = 3 emit photons that are at exactly the same wavelengths as those to nf = 2.
Problem 41b
The visible emission lines observed by Balmer all involved nf = 2. (b) Calculate the wavelengths of the first three lines in the Balmer series—those for which ni = 3, 4, and 5—and identify these lines in the emission spectrum shown in Figure 6.11.
Problem 42a
The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (a) Determine the region of the electromagnetic spectrum in which the lines of the Lyman series are observed.
Problem 42b
The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (b) Calculate the wavelengths of the first three lines in the Lyman series—those for which ni = 2, 3, and 4.
Problem 43a
One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm. a. In what region of the electromagnetic spectrum is this emission found?
Problem 43b
One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm. b. Determine the initial and final values of n associated with this emission.
Problem 44b
The hydrogen atom can absorb light of wavelength 1094 nm. (b) Determine the final value of n associated with this absorption.
Problem 45
Order the following transitions in the hydrogen atom from smallest to largest frequency of light absorbed: n = 3 to n = 6, n = 4 to n = 9, n = 2 to n = 3, and n = 1 to n = 2.
Problem 47a
Use the de Broglie relationship to determine the wavelengths of the following objects: (a) an 85-kg person skiing at 50 km/hr (b) a 10.0-g bullet fired at 250 m/s
Problem 47c,d
Use the de Broglie relationship to determine the wavelengths of the following objects: (c) a lithium atom moving at 2.5 × 105 m/s (d) an ozone (O3) molecule in the upper atmosphere moving at 550 m/s.
Problem 48
Among the elementary subatomic particles of physics is the muon, which decays within a few microseconds after formation. The muon has a rest mass 206.8 times that of an electron. Calculate the de Broglie wavelength associated with a muon traveling at 8.85 * 105 cm/s.
Problem 49
Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron needed to achieve a wavelength of 1.25 Å. The mass of a neutron is 1.675×10−27 kg.
Problem 51a
Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of (a) a 1.50-mg mosquito moving at a speed of 1.40 m/s if the speed is known to within {0.01 m/s;
Ch.6 - Electronic Structure of Atoms