Solution: The hydrogen atom is composed of one proton in the nucleus and one electron

Chapter 8, Problem 21

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The hydrogen atom is composed of one proton in the nucleus and one electron, which moves about the nucleus. In the quantum theory of atomic structure, it is assumed that the electron does not move in a well-defined orbit. Instead, it occupies a state known as an orbital, which may be thought of as a cloud of negative charge surrounding the nucleus. At the state of lowest energy, called the ground state, or 1s-orbital, the shape of this cloud is assumed to be a sphere centered at the nucleus. This sphere is described in terms of 1. (a) How is the length of a curve defined? (b) Write an expression for the length of a smooth curve given by y fsxd, a < x < b. (c) What if x is given as a function of y? 2. (a) Write an expression for the surface area of the surface obtained by rotating the curve y fsxd, a < x < b, about the x-axis. (b) What if x is given as a function of y? (c) What if the curve is rotated about the y-axis? 3. Describe how we can find the hydrostatic force against a vertical wall submersed in a fluid. 4. (a) What is the physical significance of the center of mass of a thin plate? (b) If the plate lies between y fsxd and y 0, where a < x < b, write expressions for the coordinates of the center of mass. 5. What does the Theorem of Pappus say? the probability density function psrd 4 a0 3 r 2 e22rya0 r > 0 where a0 is the Bohr radius sa0 < 5.59 3 10211 md. The integral Psrd y r 0 4 a0 3 s 2 e22sya0 ds