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DERIVING THE BOHR MODEL OF THE HYDROGEN ATOM
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This doesn't explicitly appear on many school-level syllabuses nowadays, but it does make a nice extended algebraic exercise which has major historical importance. If you search on-line, you will find most derivations are aimed at undergraduate level which can often be unhelpful for school Physics pupils. This worksheet gives a short historical preamble before taking pupils through it step-by-step (though they will need to have done basic electric fields first) before ending with a historical postlude:
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