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Chapter 37: Q. 4 (page 1081)
Two of the wavelengths emitted by a hydrogen atom are and.
a. What are the and values for each of these wavelengths?
b. For each of these wavelengths, is the light infrared, visible, or ultraviolet?
a. For and .
Forand.
b. 1) Ultraviolet
2) Infrared
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Write the symbol for an atom or ion with:
a. five electrons, five protons, and six neutrons.
b. five electrons, six protons, and eight neutrons.
Consider an oil droplet of mass m and charge q. We want to determine the charge on the droplet in a Millikan-type experiment. We will do this in several steps. Assume, for simplicity, that the charge is positive and that the electric field between the plates points upward.
a. An electric field is established by applying a potential difference to the plates. It is found that a field of strength will cause the droplet to be suspended motionless. Write an expression for the droplet鈥檚 charge in terms of the suspending field and the droplet鈥檚 weight mg.
b. The field is easily determined by knowing the plate spacing and measuring the potential difference applied to them. The larger problem is to determine the mass of a microscopic droplet. Consider a mass m falling through a viscous medium in which there is a retarding or drag force. For very small particles, the retarding force is given by where b is a constant and v the droplet鈥檚 velocity. The sign recognizes that the drag force vector points upward when the droplet is falling (negative v). A falling droplet quickly reaches a constant speed, called the terminal speed. Write an expression for the terminal speed in terms of m, g, and b.
c. A spherical object of radius r moving slowly through the air is known to experience a retarding force where is the viscosity of the air. Use this and your answer to part b to show that a spherical droplet of density r falling with a terminal velocity has a radius
d. Oil has a density . An oil droplet is suspended between two plates 1.0 cm apart by adjusting the potential difference between them to 1177 V. When the voltage is removed, the droplet falls and quickly reaches constant speed. It is timed with a stopwatch, and falls 3.00 mm in 7.33 s. The viscosity of air is . What is the droplet鈥檚 charge?
e. How many units of the fundamental electric charge does this droplet possess?
A -long train is heading for an -long tunnel. If the train moves sufficiently fast, is it possible, according to Experimenters on the ground, for the entire train to be inside the tunnel at one instant of time? Explain.
The electric field in a region of space is , where is in meters.
a. Graph versus over the region .
b. Find an expression for the potential at position . As a reference, let at the origin.
c. Graph versus over the region
Express in (or or if more appropriate):
a. The kinetic energy of an electron moving with a speed of .
b. The potential energy of an electron and a proton apart.
c. The kinetic energy of a proton that has accelerated from rest through a potential difference of .
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