Speed of an electron in Bohr's orbit for Hydrogen atom is The corresponding speed of the electron in orbit, in m/s is [2023]

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Solution

Q.
Speed of an electron in Bohr's $7^{th}$ orbit for Hydrogen atom is $3.6 \times 10^{6} m/s.$ The corresponding speed of the electron in $3^{rd}$ orbit, in m/s is [2023]

1 $1.8 \times 10^{6}$

2 $7.5 \times 10^{6}$

3 $3.6 \times 10^{6}$

4 $8.4 \times 10^{6}$

Ans.
(4)

$V_{n} \propto \frac{Z}{n}$

$z = 1$

$∴$ $V_{n} \propto \frac{1}{n}$

$∴$ $\frac{V_{3}}{V_{7}} = \frac{7}{3}$

$∴$ $V_{3} = \frac{7}{3} V_{7} = \frac{7}{3} \times 3.6 \times 10^{6} m/s = 8.4 \times 10^{6} m/s$

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