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dimensional_analysis_2

dimensional_analysis_2 - Dimensional Analysis for...

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Dimensional Analysis for Hydrogen-Like Atoms In this example we are considering atoms with a heavy nuclear charge of + Ze ( Z is the number of protons) with total mass M nucl , and a single electron with charge - e and mass m e M nucl . We’ll apply the procedure for doing systematic dimensional analysis that was presented in an earlier handout to find out about the characteristic size of the radius and energy. General Procedure 1. Determine the relevant quantities from physics considerations, often based on the equation(s) that determine how the system behaves. 2. Determine the fundamental units (e.g., [ M ], [ L ], [ T ]) of each quantity. 3. Postulate an equation relating the quantities, with unknown exponents ( a , b , . . . ). 4. Substitute units. 5. Equate exponents of [ M ], [ L ], [ T ] and solve the resulting equations simultaneously. 6. Check your results by plugging back into the equations. Check whether the physics makes sense. Ok, now we apply the steps . . .
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