Do you think you found all of the solutions of the first equation? If you want to be fussy, there is also a small amount of screening by the 2s electrons in fluorine and by the 3s electrons in chlorine.
Fluorine is much more reactive than chlorine despite the lower electron affinity because the energy released in other steps in its reactions more than makes up for the lower amount of energy released as electron affinity.
Why is fluorine out of line? These factors are discussed in more detail on that page than they are on this one. If you already know the solution, you can tell immediately whether the number inside the absolute value brackets is positive or negative, and you can drop the absolute value brackets.
The incoming electron is going to be closer to the nucleus in fluorine than in any other of these elements, so you would expect a high value of electron affinity. Plug these values into both equations. For a random number x, both the following equations are true: Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets.
Finds only one of the solutions of the first equation. Ask the student to solve the equation and provide feedback. However, comparing chlorine and bromine, say, makes things seem more difficult because of the more complicated electronic structures involved.
Examples of Student Work at this Level The student correctly writes and solves the first equation: If you plot the above two equations on a graph, they will both be straight lines that intersect the origin.
If needed, clarify the difference between an absolute value equation and the statement of its solutions.
The greater the distance, the less the attraction and so the less energy is released as electron affinity. What is the difference? Instructional Implications Provide feedback to the student concerning any errors made. For example, a fluorine atom has an electronic structure of 1s22s22px22py22pz1.
First electron affinity and reactivity The reactivity of the elements in group 7 falls as you go down the group - fluorine is the most reactive and iodine the least.
What are these two values? Should you use absolute value symbols to show the solutions? Questions Eliciting Thinking How many solutions can an absolute value equation have?
This is solution for equation 1. Set Up Two Equations Set up two separate and unrelated equations for x in terms of y, being careful not to treat them as two equations in two variables: It has 9 protons in the nucleus. By contrast, chlorine has the electronic structure 1s22s22p63s23px23py23pz1.
The amount of screening is the same in both. This means that any equation that has an absolute value in it has two possible solutions.
To solve this, you have to set up two equalities and solve each separately. A difference is described between two values. This is the solution for equation 2. Writing an Equation with a Known Solution If you have values for x and y for the above example, you can determine which of the two possible relationships between x and y is true, and this tells you whether the expression in the absolute value brackets is positive or negative.
The factors which affect this attraction are exactly the same as those relating to ionisation energies - nuclear charge, distance and screening. This is more easily seen in symbol terms. However, because fluorine is such a small atom, you are putting the new electron into a region of space already crowded with electrons and there is a significant amount of repulsion.
Guide the student to write an equation to represent the relationship described in the second problem. When you take the absolute value of a number, the result is always positive, even if the number itself is negative.
At GCSE the impression is sometimes given that the fall in reactivity is because the incoming electron is held less strongly as you go down the group and so the negative ion is less likely to form.
You are forcing an electron into an already negative ion.The equation of motion of an electron R.F. O’Connell The equation of motion of a radiating electron is a subject of recurring interest, and in particular, is dis- This enabled us to write down the equation of motion of an electron with charge e and bare mass m.
Given the factorization in terms of these matrices, one can now write down immediately an equation The transformation U is unique up to a multiplicative factor of absolute value 1. The Dirac Equation. Texts and Monographs in Physics. Solved: Write and absolute value equation that has the given solutions of x=3 and x=9 - Slader/5(1).
The electron affinity is a measure of the attraction between the incoming electron and the nucleus - the stronger the attraction, the more energy is released. The factors which affect this attraction are exactly the same as those relating to ionisation energies - nuclear charge, distance and screening.
Sal solves a word problem about a carpenter by writing an appropriate absolute value inequality and solving it. How to Write an Absolute-Value Equation That Has Given Solutions By Chris Deziel; Updated April 25, You can denote absolute value by a pair of vertical lines bracketing the number in question.Download