Atoms & Nuclei

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62 of 239

Question 62 of 239

The ratio for the speed of the electron in the 3rd{3}^{rd} orbit of He+{He}^{+} to the speed of the electron in the 3rd{3}^{rd} orbit of hydrogen atom will be :

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Answer: (D) 2:12:1

The speed of electron is given by v=2.18×106×Znms−1v=2.18\times {10}^{6}\times \dfrac{Z}{n}m{s}^{-1}, where, ZZ is atomic number and nn is number of orbit.
Now, for third orbit, ratio of speed of electron is vHvHe+=ZHZHe+=12\dfrac{{v}_{H}}{{v}_{{He}^{+}}}=\dfrac{{Z}_{H}}{{Z}_{{He}^{+}}}=\dfrac{1}{2}
⇒vHe+vH=21\Rightarrow \dfrac{{v}_{{He}^{+}}}{{v}_{H}}=\dfrac{2}{1}

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