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# Find out the number of waves made by a Bohr electron in one complete revolution in its third orbit

$(a)\;2\qquad(b)\;3\qquad(c)\;1\qquad(d)\;4$

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A)
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$r_n$ for H=$r_1\times n^2$
$r_3$ for $H=0.529\times 9\times 10^{-8}cm$
$r_1=0.529A^{\circ}$
Also $u_n=\large\frac{u_1}{n}$
$u_3=\large\frac{2.19\times 10^8}{3}$cm/s
$\therefore$No of waves in one round=$\large\frac{2\pi r_3}{\lambda}$
$\Rightarrow \large\frac{2\pi r_3}{h/mu_3}$
$\Rightarrow \large\frac{2\pi r_3\times u_3\times m}{h}$
$\Rightarrow \large\frac{2\times 22 \times 0.529\times 9\times 10^{-8}\times 2.19\times 10^8\times 9.108\times 10^{-28}}{7\times 3\times 6.62\times 10^{-27}}$
$\Rightarrow 3$
Hence (b) is the correct answer.