Option 3 : \(\frac{{20}}{7}\lambda \)
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When electron jumps from higher orbit to lower orbit then, wavelength of emitted photon is given by,
\(\frac{1}{\lambda } = R\left( {\frac{1}{{n_f^2}} - \frac{1}{{n_i^2}}} \right)\)
So, \(\frac{1}{\lambda } = R\left( {\frac{1}{{{2^2}}} - \frac{1}{{{3^2}}}} \right) = \frac{{5R}}{{36}}\)
and \(\frac{1}{{\lambda '}} = R\left( {\frac{1}{{{3^2}}} - \frac{1}{{{4^2}}}} \right) = \frac{{7R}}{{144}}\)
∴ \(\lambda ' = \frac{{144}}{7} \times \frac{{5\lambda }}{{36}} = \frac{{20\lambda }}{7}\)
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When an electron in a hydrogen atom jumps from the third orbit to the second orbit, it emits a photon of wavelength 'λ'. When it jumps from the fourth orbit to third orbit, the wavelength emitted by the photon will be ______.
`20/7lambda`
`16/25lambda`
`20/13lambda`
`9/16lambda`
When an electron in a hydrogen atom jumps from the third orbit to the second orbit, it emits a photon of wavelength 'λ'. When it jumps from the fourth orbit to third orbit, the wavelength emitted by the photon will be `underline(20/7lambda)`.
Explanation:
`1/lambda=R(1/2^2-1/3^2)=R(1/4-1/9)=(Rxx5)/36`
`1/lambda^'=R(1/3^2-1/4^2)=R(1/9-1/16)=Rxx7/144`
`lambda^'/lambda=5/36xx144/7=20/7`
`thereforelambda^'=20/7lambda`
Concept: Bohr’s Atomic Model
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