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- List the following types of electromagnetic radiation in order of increasing wavelength: (a) the gamma rays produced by a radioactive nuclide used in medical imaging; (b) radiation from an FM radio station at 93.1 MHz on the dial; (c) a radio signal from an AM radio station at 680 kHz on the dial; (d) the yellow light from sodium vapor streetlights; (e) the red light of a light-emitting diode, such as in a calculator display.
Problem 18
Problem 19a
(a) What is the frequency of radiation that has a wavelength of 10 µm, about the size of a bacterium?
Problem 19b
(b) What is the wavelength of radiation that has a frequency of 5.50 × 1014 s-1?
Problem 20c
(c) Would the radiations in part (a) or part (b) be detected by an X-ray detector?
Problem 20d
(d) What distance does electromagnetic radiation travel in 0.38 ps?
Problem 21a
A laser pointer used in a lecture hall emits light at 650 nm. What is the frequency of this radiation?
Problem 21b
A laser pointer used in a lecture hall emits light at 650 nm. Using Figure 6.4, predict the color associated with this wavelength.
Problem 22
It is possible to convert radiant energy into electrical energy using photovoltaic cells. Assuming equal efficiency of conversion, would infrared or ultraviolet radiation yield more electrical energy on a per-photon basis?
Problem 23
If human height were quantized in 1-cm increments, what would happen to the height of a child as she grows up: (i) the child's height would never change, (ii) the child's height would continuously increase, (iii) the child's height would increase in jumps of 6 cm, or (iv) the child's height would increase in 'jumps' of 1 cm at a time?
- Einstein's 1905 paper on the photoelectric effect was the first important application of Planck's quantum hypothesis. Describe Planck's original hypothesis, and explain how Einstein made use of it in his theory of the photoelectric effect.
Problem 24
Problem 25a
(a) Calculate the energy of a photon of electromagnetic radiation whose frequency is 2.94 × 1014 s-1.
Problem 25b
(b) Calculate the energy of a photon of radiation whose wavelength is 413 nm.
Problem 25c
(c) What wavelength of radiation has photons of energy 6.06 × 10-19 J?
Problem 26a
(a) A green laser pointer emits light with a wavelength of 532 nm. What is the frequency of this light?
Problem 26b
(b) What is the energy of one of these photons?
Problem 26c
(c) The laser pointer emits light because electrons in the material are excited (by a battery) from their ground state to an upper excited state. When the electrons return to the ground state, they lose the excess energy in the form of 532-nm photons. What is the energy gap between the ground state and excited state in the laser material?
- (a) Calculate and compare the energy of a photon with a wavelength of 3.0 mm to that of a photon with a wavelength of 0.3 nm.
Problem 27
Problem 28
An AM radio station broadcasts at 1000 kHz and its FM partner broadcasts at 100 MHz. Calculate and compare the energy of the photons emitted by these two radio stations.
Problem 29a
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (a) What is the energy of a photon of this wavelength?
Problem 29b
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (b) What is the energy of a mole of these photons?
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 rupture chemical bonds. A minimum energy of 192 kJ/mol is required to break the bromine–bromine bond in Br2. 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 3.0 mm. (a) What type of electromagnetic spectrum is this radiation (b) If a detector is capturing 3.0 3 108 photons per second at this wavelength, what is the total energy of the photons detected in 1 day?
Problem 33a
Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (a) What is the frequency threshold for emission of electrons?
Problem 33b
Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') 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 an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (c) If molybdenum is irradiated with light of wavelength of 240 nm, what is the maximum possible velocity 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?