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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 39b
List these types of electromagnetic radiation in order of (ii) increasing energy per photon.
a. visible light
b. radio waves
c. X-ray
d. ultraviolet radiation
Problem 40
List these types of electromagnetic radiation in order of (i) increasing frequency and (ii) decreasing energy per photon.
a. gamma rays
b. ultraviolet radiation
c. infrared radiation
d. microwaves
Problem 41
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 43
Calculate the energy of a photon of each wavelength and state what part of the electromagnetic spectrum is associated with the wavelength.
a. 105 nm
b. 715 nm
c. 2.52 cm
Problem 44
Calculate the energy of a photon of each frequency and state what part of the electromagnetic spectrum is associated with the frequency.
a. 15.77×1017 Hz
b. 1.18×1014 Hz
c. 3.00×1020 Hz
Problem 45
A laser pulse with wavelength 532 nm contains 1.85 mJ of energy. How many photons are in the laser pulse?
Problem 46
A heat lamp produces 17.7 watts of power at a wavelength of 6.5 μm. How many photons are emitted per second? (1 watt = 1 J/s)
Problem 47a
Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) a. infrared radiation (1500 nm)
Problem 48
How much energy is contained in 1 mol of each? a. X-ray photons with a wavelength of 0.135 nm b. g-ray photons with a wavelength of 2.15 * 10-5 nm
Problem 49
Sketch the interference pattern that results from the diffraction of electrons passing through two closely spaced slits.
Problem 51
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 52
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.
Problem 54
A proton in a linear accelerator has a de Broglie wavelength of 132 pm. What is the speed of the proton?
Problem 55
Calculate the de Broglie wavelength of a 143-g baseball traveling at 85 mph. Is the wave nature of matter significant for a baseball?
Problem 56
A 0.22-caliber handgun fires a 1.9-g bullet at a velocity of 745 m/s. Calculate the de Broglie wavelength of the bullet. Is the wave nature of matter significant for bullets?
Problem 57
An electron has an uncertainty in its position of 552 pm. What is the uncertainty in its velocity?
Problem 58
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?
Problem 60
Which electron is, on average, farther from the nucleus: an electron in a 3p orbital or an electron in a 4p orbital?
Problem 61
What are the possible values of l for each given value of n? a. 1 b. 2 c. 3 d. 4
Problem 62a
What are the possible values of ml for each value of l? a. 0
Problem 62b
What are the possible values of ml for each value of l? b. 1
Problem 62c
What are the possible values of ml for each value of l? c. 2
Problem 63
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 64
Which combinations of n and l represent real orbitals, and which do not exist? a. 1s b. 2p c. 4s d. 2d
Problem 69
Sketch the 1s and 2p orbitals. How do the 2s and 3p orbitals differ from the 1s and 2p orbitals?
Problem 70
Sketch the 3d orbitals. How do the 4d orbitals differ from the 3d orbitals?
Problem 72
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
Problem 74
According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with the longer wavelength: 3p¡2s or 4p¡3p ?
