question_answer

In \[L{{i}^{++}},\]electron in first Bohr orbit is excited to a level by a radiation of wavelength\[\lambda .\] when the ion gets 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 \[\lambda \]?

(Given : \[h=6.63\times {{10}^{34\text{ }}}Js;c=3\times {{10}^{8}}m{{s}^{1}}\])

[JEE Main 10-4-2019 Afternoon]

A) 9.4 nm                        

B) 12.3 nm

C) 10.8 nm

D) 11.4 nm

Correct Answer: C

Solution :

  \[\Delta E=\frac{hc}{\lambda }\] \[13.6\times 9-0.85\times 9=\frac{hc}{\lambda }\] \[\lambda =\frac{hc}{9\times (13.6-0.85)eV}\] \[=\frac{1240eV.nm}{9\times 12.75eV}\] \[\lambda =10.8nm\]