CHEM1101 Worksheet 3: The Energy Levels Of Electrons

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1 CHEM1101 Woksheet 3: The Enegy Levels Of Electons Model 1: Two chaged Paticles Sepaated by a Distance Accoding to Coulomb, the potential enegy of two stationay paticles with chages q 1 and q 2 sepaated by a distance is: V = k whee k is a positive-valued popotionality constant. Citical thinking questions 1. What happens to the magnitude of V if is inceased? paticle 1: chage = q 1 paticle 2: chage = q 2 2. What is the value of V if the paticles ae sepaated by an infinite distance (i.e. = )? 3. Is V < 0 o is V > 0 if the paticles have the same chage? 4. If q = -1 fo an electon, what is q fo a poton? 5. A hydogen atom consists of an electon obiting aound a poton. Is the potential enegy of a hydogen atom positive o negative? 6. Using you answes to questions 2 and 5, descibe in wods what happens to the potential enegy of a hydogen atom as its electon is emoved (i.e. the atom is ionized)? 7. The pictue opposite shows two electons and a helium nucleus aanged in a staight line. electon 1 nucleus electon 2 Wite down the total potential enegy of this aangement as a sum of thee tems

2 Model 2: Electon Enegy Fo an atom, such as hydogen, with one electon obiting aound a nucleus with chage Z, the enegy of the electon is given by the equation below: E n = ( J) whee n = 1, 2, 3, 4... The diffeent values of n coespond to the allowed enegies that the electon can have. These enegies ae called enegy levels. The lowest enegy level has n = 1 and is called the gound state. All othe enegy levels ae called excited states. The aveage size of the electon s obit ae also contolled by the value of n: aveage = ( m) Citical thinking questions 8. The hydogen atom has atomic numbe Z = 1. Using the equations above fo the enegy and aveage adius of electon s obit, complete the table below fo hydogen. n E n (J) aveage (m) The hoizontal lines on the gaph on the left hand side of last page of this woksheet shows the enegy levels fo n = 1, 2 and 3. Using the values you calculated fo E n, add the enegy levels fo n = Descibe in wods to you neighbou what happens to the enegy levels and the aveage size of the obit as n inceases. When you have ageed on this, wite down you desciption in a gammatically coect sentence below. 11. What do you pedict is the limiting behaviou of the enegy and obit of the electon when n appoaches infinity?

3 Model 3: Atomic Spectoscopy THE ENERGY LEVELS OF ELECTRONS The electon in a H atom wandeing aound in space will be in the n = 1 level (the gound state ). Howeve, if a high voltage is passed though H 2 molecules, an excited H atom is fomed in which the electon is in a level with n > 1. The electon in this excited atom quickly moves ( elaxes ) to a lowe level and the excess enegy is lost ( emitted ) as adiation. Fo example, if the excited atom is fomed with its electon in the n = 3 level, the electon can fall into the n = 2 o into the n = 1 level. This is shown by the dotted vetical lines on the gaph. The enegy lost as adiation is the diffeence between the two enegy levels involved: it is equal to the length of the dotted line. If the electon moves fom (a) n = 3 to n = 1, the enegy emitted is equal to and (b) n = 3 to n = 2, the enegy emitted is equal to J. These enegies can be measued on the gaph o calculated using the values in the table on question 8. The enegy of the emitted adiation fo jumps (a) and (b) is shown by the hoizontal lines on the gaph of the ight hand side oveleaf. Citical thinking questions 12. If the excited atom is fomed with the electon in the n = 4 level, add dotted lines to the gaph showing how the electon can elax. 13. Fo each of these jumps, wok out the enegy of the emitted adiation and mak it using a hoizontal line on the ight hand gaph. 14. Repeat question 13 fo an excited atom fomed with the electon in the n = 5 level. 15. The ight hand gaph epesents the enegy of the emitted adiation fo the hydogen atom. You have dawn its atomic spectum. Light with enegy less than is the infaed egion. Light with enegy geate than J is ultaviolet. Visible light lies between these values. Mak these egions on you spectum. 16. (a) What wavelengths coespond to the uppe and lowe limits of visible light given in Q15? (b) What colous coespond to these limits? 17. What do the lines in the visible pat of the spectum have in common? 18. What do the lines in the ultaviolet pat of the spectum have in common? colou ed oange yellow geen blue indigo violet wavelength (nm)

4 0 Enegy levels of the H atom Atomic Spectum of the H atom 250 (a) (b) n = 3 50 n = 2 (a) 200 enegy J adiation enegy J n = 1 (b) 250 0

5 THE ENERGY LEVELS OF ELECTRONS

Nuclear and Particle Physics - Lecture 20 The shell model

Nuclear and Particle Physics - Lecture 20 The shell model 1 Intoduction Nuclea and Paticle Physics - Lectue 0 The shell model It is appaent that the semi-empiical mass fomula does a good job of descibing tends but not the non-smooth behaviou of the binding enegy.