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Relating Translational KE and T

n → Orbit n...

Question

n $\to$ Orbit no.,\, Z $\to$ Atomic no $⟹ r n, x \to$ Radius $v_{n, z} \to$ velocity
$T_{n, z} \to$ time period of Revolution $⟹ K_{n, z} \to$ Kinetic energy of the electron

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Solution

(a) $r = 0.521 \times \frac{n^{2}}{z} A^{\circ}$
(b) $V = 2 / 18 \times 10^{6} z / n$
(c) $T \propto n^{3} / z^{2}$
(d) $K . E \propto \frac{Z^{2}}{n^{2}}$

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