Question

Calculate the frequency of light emitted when an electron transitions from sixth to the second orbit of the hydrogen atom. In what region of spectrum does this light occur?

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Solution

space space 1 over straight lambda space equals space straight R open square brackets fraction numerator 1 over denominator straight n subscript 1 superscript 2 end fraction minus fraction numerator 1 over denominator straight n subscript 2 superscript 2 end fraction close square brackets space straight n subscript 1 space equals space 2 comma space space space straight n subscript 2 space equals space 6 comma space space space straight R space equals space 109677 space c m to the power of negative 1 end exponent

space space space space space therefore space space space space space 1 over straight lambda space equals space 109677 space open square brackets 1 fourth minus 1 over 36 close square brackets space space space space space space space space space space space space space space space equals 109677 space cross times space 6.22222 space space space space space space space space space space space space space space space space equals 24370 space c m to the power of negative 1 end exponent

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space equals 3 space cross times space 10 to the power of 10 cms to the power of negative 1 end exponent cross times 24370 left parenthesis cm to the power of negative 1 end exponent right parenthesis

space space space space space space space equals space 7.31 space cross times space 10 to the power of 14 s e c to the power of negative 1 end exponent

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Structure Of Atom

Calculate the frequency of light emitted when an electron transitions from sixth to the second orbit of the hydrogen atom. In what region of spectrum does this light occur?

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