Note for CHEM 201H at OSU
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Date Created: 02/06/15
Chemistry 201H 7 Problem Set 1 Due Friday October 1 in class Textbook problems 110 112 114 128 130 132 134 Additional problems 1 The green laser pointer that I use in class emits light whose wavelength is 531 nm This laser has 50 mW of power The Watt W is the SI unit for power By de nition 1 W 1 Js Suppose that I turn on this pointer for 3 seconds How many photons of green light are emitted during this time 2 When a certain metal is irradiated with 251 nm light electrons are emitted with a maximum kinetic energy of 142 eV Here eV is the electron volt a common unit of energy in chemistry and physics which is equal to the kinetic energy of an electron that is accelerated through an electric potential difference of one volt a What is the work function of the metal in eV b What is the de Broglie wavelength associated with the ejected electrons whose kinetic en ergy is 142 eV Here and elsewhere you may need to look up appropriate unit conversion factors 3 An excited hydrogen atom emits light whose wavelength is 2625 nm a To which region of the electromagnetic spectrum does this light correspond b What is the frequency of the light in Hertz Hz c The quantity 1 is known as the wave number of a given wave For electromagnetic radiation prove without plugging in any numbers that 1 is proportional to the energy of the wave d Evaluate the wave number for the aforementioned hydrogen atom emission line in units of cm l Units of cm 1 are sometimes called wave numbers although in reality any units of inverse length could correctly be called wave numbers In view of 3c the energy of electromagnetic radiation can be expressed in units of cm l and these units are often used in the context of infrared spectroscopy e What is the energy of these 2625 nm photons in units of kJmol 4 Both electron diffraction discussed in class and neutron diffraction for which C G Schull was awarded the Nobel Prize in Physics in 1994 are important techniques for elucidating the atomic level structure of crystalline materials a Calculate the de Broglie wavelength of a neutron moving at 100 of the speed of light b Calculate the velocity of a neutron whose wavelength is 75 pm Note pm picometers c Calculate the wavelength of an electron that is accelerated from rest through a potential difference of 100 kV d As the speed of an object 239e matter approaches the speed of light relativistic effects as in Einstein s theory of relativity become increasingly important The expression p mm for linear momentum is actually the non relativistic U ltlt 0 limit of the more general expression mi 19 Ml 711262 How will relativistic effects alter the wavelengths that you calculated in 4a and 4c Try to answer this question using the appropriate formulas without plugging in actual numbers Consider a particle in a onedimensional box of length L which extends from x 0 to z L For the n 4 quantum state a What is or are the most probable locations of the particle b What is the probability of nding the particle in the left most quarter of the box 239e 0 g x L4 This question could be answered by evaluating an appropriate integral but a simpler solution is to graph the appropriate function and answer the question by inspection of the graph An electron in a onedimensional box whose length is 100 nm is excited from the ground state into a higher energy state by absorbing a photon whose wavelength is 1374 x 10 5 m a Determine the energy of the excited state in question b Determine the quantum number for the excited state in question
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