Atoms & Nuclei

JEE Main level, single correct, medium

57 of 239

Question 57 of 239

Speed of an electron in Bohr’s 7th{7}^{th} orbit for Hydrogen atom is 3.6×106ms−13.6\times {10}^{6}m{s}^{-1}. The corresponding speed of the electron in 3rd{3}^{rd} orbit, in ms−1m{s}^{-1} is :

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Answer: (D) 8.4×1068.4\times {10}^{6}

For hydrogen like atom, the velocity of electron in nth{n}^{th} orbit is given by
v=z2e22ϵ0hnv=\dfrac{{z}^{2}{e}^{2}}{2{\epsilon }_{0}hn}
∴v∝1n∴v\propto \dfrac{1}{n}
⇒v1v2=n2n1\Rightarrow \dfrac{{v}_{1}}{{v}_{2}}=\dfrac{{n}_{2}}{{n}_{1}}
⇒3.6×106v2=37\Rightarrow \dfrac{3.6\times {10}^{6}}{{v}_{2}}=\dfrac{3}{7}
v2=8.4×106ms−1{v}_{2}=8.4\times {10}^{6}m{s}^{-1}

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