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How many times does species will have same radius as that Bohr’s orbit hydrogen in one second?

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$0.657 \times 10^{15}$

$6.57 \times 10^{10}$

$65.7 \times 10^{12}$

$6.57 \times 10^{15}$

answer is B.

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Detailed Solution

For H – atom, $V_{1}$ $V_{1} = \frac{2 π e^{2}}{h}, r_{1} = \frac{h^{2}}{4 π^{2} m e^{2}}$

$∴$ Circumference of 1^st Bohr orbit = $2 π r_{1}$

$= \frac{2 π h^{2}}{4 π^{2} m e^{2}} = \frac{h^{2}}{2 π m e^{2}}$

$∴$ Number of rounds by electrons in 1^st orbit

$= \frac{v_{1}}{2 π r_{1}} = \frac{2 π e^{2} \times 2 π m e^{2}}{h \times h^{2}} = \frac{4 π^{2} m e^{2}}{h^{3}}$

$= 6.57 \times 10^{15} r o u n d / s$

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