Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Transcribed Image Text:1) Calculate the energy of one mole of UV photons of wavelength 300 nm and compare it with a typical
single-bond energy of 400 kJ/mol.
2) Calculate the de Broglie wavelength of an electron moving at 1/137th the speed of light.
3) Calculate the radius of Bohr's fifth orbit for hydrogen atom.
4) The electron energy in hydrogen atom is given by En = (-2.18 x 10 -18)/n² J. Calculate the energy
required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of
light in cm that can be used to cause this transition?
5) Simplify (a) i2; (b) i3; (c) i*; (d) i*i; (e) (1+ 51)(2 - 37); (f) (1 - 3i)/(4 + 2i). Hint: In (f), multiply numerator
and denominator by the complex conjugate of the denominator.
6) At a certain instant of time, a one-particle, one-dimensional system has Y = (2/b3)/2 xe-lx//b
where b = 3.000 nm. If a measurement of x is made at this time in the system, find the probability
that the result
(a) Lies between 0.9000 nm and 0.9001 nm (treat this interval as infinitesimal).
(b) Lies between 0 and 2 nm (use the integral below).
(c) For what value of x is the probability density a minimum? (There is no need to use calculus to
answer this.)
(d) Verify that Y is normalized.
7) Consider a particle with quantum number n moving in a one-dimensional box of length I.
(a) Find the probability of finding the particle in the left quarter of the box. (b) For what value of n is
this probability a maximum? (c) What is the limit of this probability for n→ o?
8) For the particle confined to a 2-D box, find the following values for the state with quantum numbers
n (a) <x>; (b) <x?>; (c) <p,>; (d) <p,?>; Is <x'> = <x>? Is <p,?>=<p,>?
2 2r
n!
redx
n>-1, q > 0
1
sin bx dx =- sin(2hx)
4b
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