The wave length of radiation emitted when an electron in hydrogen atom drops from sixth orbit to fifth orbit is
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The wave length of radiation emitted when an electron in hydrogen atom drops from sixth orbit to fifth orbit is
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Answer:
the wave length of radiation
To find:
Wave length of radiation emitted when an electron in hydrogen atom drops from sixth orbit to fifth orbit ?
Calculation:
Applying Rydberg's Formula for wavelength of radiation due to electron's change in orbit:
[tex] \therefore \: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{1}{ { (n_{f})}^{2} } - \dfrac{1}{ {(n_{i})}^{2} } \bigg][/tex]
Now , n_(f) = 5 and n_(i) = 6 (as per question):
[tex] \implies\: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{1}{ { (5)}^{2} } - \dfrac{1}{ {(6)}^{2} } \bigg][/tex]
[tex] \implies\: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{1}{25} - \dfrac{1}{36} \bigg][/tex]
[tex] \implies\: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{36 - 25}{25 \times 36} \bigg][/tex]
[tex] \implies\: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{11}{25 \times 36} \bigg][/tex]
[tex] \implies\: \dfrac{1}{ \lambda} = R \bigg[ \dfrac{11}{900} \bigg][/tex]
[tex] \implies\: \lambda= \dfrac{900}{11 R}[/tex]
So , the wavelength is 900/(11R).