Atoms & Nuclei

JEE Main level, single correct, medium

72 of 239

Question 72 of 239

InLi++L{i}^{++},electron in first Bohr orbit is excited to a level by a radiation of wavelengthλ\lambda.When the ion gets de excited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of λ\lambda ?

(Given: h=6.63×10−34Js;c=3×108ms−1h=6.63\times {10}^{-34}Js;c=3\times {10}^{8}m{s}^{-1} )

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Answer: (A) 10.8nm10.8nm

Total Number of possible spectral lines that can be emmited when atom de-excites from state nnto groundstate is C2nC2n
∴nC2=6⇒n(n−1)2=6⇒n=4∴{}^{n}{C}_{2}=6\Rightarrow \dfrac{n(n-1)}{2}=6\Rightarrow n=4
1λ=Rz2(112−142)=1.097×107×9×(1−116)\dfrac{1}{\lambda }=R{z}^{2}\left(\dfrac{1}{{1}^{2}}-\dfrac{1}{{4}^{2}}\right)=1.097\times {10}^{7}\times 9\times \left(1-\dfrac{1}{16}\right)
⇒λ=10.8nm\Rightarrow \lambda =10.8nm

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