A) 9/(5R)
B) 36/(5R)
C) 18/(5R)
D) 4/R
Correct Answer: C
Solution :
In hydrogen atom \[{{E}_{n}}=-\frac{Rhc}{{{n}^{2}}}\] Also \[{{E}_{n}}\propto m\]; where m is the mass of the electron. Here the electron has been replaced by a particle whose mass is double of an electron. Therefore, for this hypothetical atom energy in nth orbit will be given by \[{{E}_{n}}=-\frac{2Rhc}{{{n}^{2}}}\] The longest wavelength \[{{\lambda }_{\max }}\] (or minimum energy) photon will correspond to the transition of particle from n = 3 to n = 2 Þ \[\frac{hc}{{{\lambda }_{\max }}}={{E}_{3}}-{{E}_{2}}=Rhc\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}} \right)\] This gives \[{{\lambda }_{\max }}=\frac{18}{5R}\].You need to login to perform this action.
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