Question:
The velocity of an electron in the second orbit of sodium atom (atomic number = 11) is \( v \). The velocity of an electron in its fifth orbit will be:
The velocity of an electron in the second orbit of sodium atom (atomic number = 11) is \( v \). The velocity of an electron in its fifth orbit will be:
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The velocity of an electron in a Bohr orbit is inversely proportional to the square root of the principal quantum number \( n \).
Updated On: Apr 22, 2026
- \( v \)
- \( \frac{22}{5}v \)
- \( \frac{5}{2}v \)
- \( \frac{2}{5}v \)
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The Correct Option is D
Solution and Explanation
Step 1: Use Bohrâs formula for electron velocity.
The velocity of an electron in a particular orbit is inversely proportional to the square root of the principal quantum number \( n \), i.e., \[ v_n \propto \frac{1}{\sqrt{n}} \]
Step 2: Calculate the velocity ratio.
For the second orbit (\( n = 2 \)) and the fifth orbit (\( n = 5 \)), the ratio of velocities is: \[ \frac{v_5}{v_2} = \frac{\sqrt{2}}{\sqrt{5}} = \frac{2}{5} \]
Step 3: Conclusion.
Thus, the velocity of the electron in the fifth orbit is \( \frac{2}{5}v \).
The velocity of an electron in a particular orbit is inversely proportional to the square root of the principal quantum number \( n \), i.e., \[ v_n \propto \frac{1}{\sqrt{n}} \]
Step 2: Calculate the velocity ratio.
For the second orbit (\( n = 2 \)) and the fifth orbit (\( n = 5 \)), the ratio of velocities is: \[ \frac{v_5}{v_2} = \frac{\sqrt{2}}{\sqrt{5}} = \frac{2}{5} \]
Step 3: Conclusion.
Thus, the velocity of the electron in the fifth orbit is \( \frac{2}{5}v \).
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