A) 2
B) 4
C) 8
D) 16
Correct Answer: A
Solution :
Idea This problem includes conceptual mixing of de-Broglie equation and energy consideration during formation of molecule. So, students are advised to calculate the energy required and energy released during process and then by using de-Broglie equation and concept of energy consideration during formation of molecule. Calculate the required parameter. \[X+2{{e}^{-}}\xrightarrow[{}]{{}}{{X}^{2-}}\]energy released = 30.86 eV Total energy released = number of moles of molecule\[\times \]energy released by one moles of molecule \[=y\times 30.86\,\text{eV}\] Number of moles of\[{{H}_{2}}=\frac{4g}{2g}=2\] \[2{{H}_{2}}\xrightarrow{{}}2{{H}^{+}}2{{H}^{+}}\] According to de-Broglie, \[2\pi r=n\lambda \Rightarrow 2\pi r=4\lambda \] Total energy required = total energy required to dissociate two moles of\[{{H}_{2}}+\]total energy required in ionization of two\[{{H}^{-}}\]to two\[{{H}^{+}}\]+ total energy required in ionization of two H to 4th excited energy level. \[=2\times 4.52\times {{N}_{A}}+2\times 13.6{{N}_{A}}+2\times 13.6\] \[\times \left( 1-\frac{1}{16} \right)\times {{N}_{A}}\] \[={{N}_{A}}(9.04+27.2+27.2\times 0.93)\] \[={{N}_{A}}(61.53)\]eV We know that during formation of\[{{H}^{+}}\]and\[{{H}^{*}}\]in above reaction. Total energy required = Total energy released \[\therefore \] \[\text{61}\text{.53}\times {{\text{N}}_{A}}\text{eV = }-\text{30}\text{.86 y eV}\] \[y=\frac{61.53}{30.86}\simeq 2\] Hence, number of moles required = 2 TEST Edge In JEE Main, this question is asked to Judge the depth of knowledge of student. So, students are advised to study the subject in such a way that question including depth of theory and concept would be solved easily. Students are advised to study the Hisenberg uncertainty principle and photoelectric effect.
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