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- Calculate the wavelength of each frequency of electromagnetic radiation, assuming four significant figures: a. 100.2 MHz (typical frequency for FM radio broadcasting) b. 1070 kHz (typical frequency for AM radio broadcasting) c. 835.6 MHz (common frequency used for cell phone communication).
Problem 4
Problem 35
The distance from the sun to Earth is 1.496×108 km. How long does it take light to travel from the sun to Earth?
Problem 36
The nearest star to our sun is Proxima Centauri, at a distance of 4.3 light-years from the sun. A light-year is the distance that light travels in one year (365 days). How far away, in km, is Proxima Centauri from the sun?
Problem 37b
List these types of electromagnetic radiation in order of (ii) increasing energy per photon. a. radio waves b. microwaves c. infrared radiation d. ultraviolet radiation
Problem 38
List these types of electromagnetic radiation in order of (i) increasing frequency and (ii) decreasing energy per photon. a. gamma rays b. radio waves c. microwaves d. visible light
Problem 39
Calculate the frequency of each wavelength of electromagnetic radiation: a. 632.8 nm (wavelength of red light from helium–neon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (wavelength contained in medical X-rays)
Problem 41
Calculate the energy of a photon of electromagnetic radiation at each of the wavelengths indicated in Problem 39. a. 632.8 nm (wavelength of red light from helium–neon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (wavelength contained in medical X-rays)
Problem 42
Calculate the energy of a photon of electromagnetic radiation at each of the frequencies indicated in Problem 40. a. 100.2 MHz (typical frequency for FM radio broadcasting) b. 1070 kHz (typical frequency for AM radio broadcasting) (assume four significant figures) c. 835.6 MHz (common frequency used for cell phone communication)
Problem 43
A laser pulse with wavelength 532 nm contains 3.85 mJ of energy. How many photons are in the laser pulse?
Problem 44
A heat lamp produces 32.8 watts of power at a wavelength of 6.5 µm. How many photons are emitted per second? (1 watt = 1 J/s)
Problem 45
Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) a. infrared radiation (1500 nm) b. visible light (500 nm) c. ultraviolet radiation (150 nm)
Problem 46
How much energy is contained in 1 mol of each? a. X-ray photons with a wavelength of 0.135 nm b. γ-ray photons with a wavelength of 2.15×10–5 nm
Problem 47
Sketch the interference pattern that results from the diffraction of electrons passing through two closely spaced slits.
- What happens to the interference pattern if we attempt to determine which slit the electron passes through using a laser placed directly behind the slits? Additionally, what happens to the interference pattern described in Problem 47 if the rate of electrons passing through the slits is reduced to one electron per hour?
Problem 48
Problem 49
The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.20 nm in modern instruments. Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.20 nm?
Problem 50
The smallest atoms can themselves exhibit quantum-mechanical behavior. Calculate the de Broglie wavelength (in pm) of a hydrogen atom traveling at 475 m/s.
- What is the de Broglie wavelength of an electron traveling at 1.35 x 10^5 m/s?
Problem 51
Problem 52
A proton in a linear accelerator has a de Broglie wavelength of 122 pm. What is the speed of the proton?
Problem 53
Calculate the de Broglie wavelength of a 143-g baseball traveling at 95 mph. Why is the wave nature of matter not important for a baseball?
Problem 54
A 0.22-caliber handgun fires a 1.9-g bullet at a velocity of 765 m/s. Calculate the de Broglie wavelength of the bullet. Is the wave nature of matter significant for bullets?
Problem 55
An electron has an uncertainty in its position of 552 pm. What is the uncertainty in its velocity?
Problem 56
An electron traveling at 3.7×105 m/s has an uncertainty in its velocity of 1.88×105 m/s. What is the uncertainty in its position?
- Which electron is, on average, closer to the nucleus: an electron in a 2s orbital or an electron in a 3s orbital?
Problem 57
Problem 58
Which electron is, on average, farther from the nucleus: an electron in a 3p orbital or an electron in a 4p orbital?
Problem 59
What are the possible values of l for each given value of n? a. 1 b. 2 c. 3 d. 4
Problem 60a
What are the possible values of ml for each value of l? a. 0
Problem 60b
What are the possible values of ml for each value of l? b. 1
Problem 60c,d
What are the possible values of ml for each value of l? c. 2 d. 3
Problem 61
Which set of quantum numbers cannot occur together to specify an orbital? a. n = 2, l = 1, ml = -1 b. n = 3, l = 2, ml = 0 c. n = 3, l = 3, ml = 2 d. n = 4, l = 3, ml = 0
Problem 62
Which combinations of n and l represent real orbitals, and which do not exist? a. 1s b. 2p c. 4s d. 2d