The velocity of an electron in the second orb | vedclass

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(D) The velocity of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by the formula $v_n = v_0 \frac{Z}{n}$,where $Z$ is the atomic

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$\frac{2}{5}v$

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(D) The velocity of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by the formula $v_n = v_0 \frac{Z}{n}$,where $Z$ is the atomic number and $n$ is the orbit number.From this relation,we can see that for a given atom (constant $Z$),the velocity is inversely proportional to the orbit number: $v_n \propto \frac{1}{n}$.Given that the velocity in the second orbit $(n_2 = 2)$ is $v$,we have $v_2 = v$.We need to find the velocity in the fifth orbit $(n_5 = 5)$,denoted as $v_5$.Using the proportionality $v_n \propto \frac{1}{n}$,we can write the ratio: $\frac{v_5}{v_2} = \frac{n_2}{n_5}$.Substituting the known values: $\frac{v_5}{v} = \frac{2}{5}$.Therefore,$v_5 = \frac{2}{5}v$.

The velocity of an electron in the second orbit of a sodium atom (atomic number $Z = 11$) is $v$. The velocity of an electron in its fifth orbit will be

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