Physics-
General
Easy

Question

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

  1. III    
  2. IV    
  3. I    
  4. II    

The correct answer is: III


    E equals R h c open square brackets fraction numerator 1 over denominator n subscript 1 end subscript superscript 2 end superscript end fraction minus fraction numerator 1 over denominator n subscript 2 end subscript superscript 2 end superscript end fraction close square brackets
    table row cell E subscript open parentheses 4 rightwards arrow 3 close parentheses end subscript equals text end text text R end text text h end text text e end text text end text open square brackets fraction numerator 1 over denominator 3 to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator 4 to the power of 2 end exponent end fraction close square brackets equals text end text text R end text text h end text text e end text text end text open square brackets fraction numerator 7 over denominator 9 cross times 16 end fraction close square brackets equals 0.05 R h c end cell row cell E subscript open parentheses 4 rightwards arrow 2 close parentheses end subscript equals open square brackets fraction numerator 1 over denominator 2 to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator 4 to the power of 2 end exponent end fraction close square brackets equals text end text text R end text text h end text text c end text text end text open square brackets fraction numerator 3 over denominator 16 end fraction close square brackets equals 0.2 R h c end cell row cell E subscript left parenthesis 2 rightwards arrow t end subscript equals R h c open square brackets fraction numerator 1 over denominator left parenthesis 1 right parenthesis to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator left parenthesis 2 right parenthesis to the power of 2 end exponent end fraction close square brackets equals R h c open square brackets fraction numerator 3 over denominator 4 end fraction close square brackets equals 0.75 R h c end cell row cell E subscript open parentheses 1 rightwards arrow 3 close parentheses end subscript equals R h c open square brackets fraction numerator 1 over denominator left parenthesis 3 right parenthesis to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator left parenthesis 1 right parenthesis to the power of 2 end exponent end fraction close square brackets equals fraction numerator 8 over denominator 9 end fraction R h c equals negative 0.9 R h c end cell end table
    \ Thus, III transition gives most energy.

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