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.You need to login to perform this action.
You will be redirected in
3 sec