Obtain An Expression For The Radius Of Bohr Orbit For

From Bohr’s second postulate,

Ln = mvrn =\( \frac{nh}{2\Pi}—[1]\)

where:

n is an integer

ris the radius of the nth possible orbit

vis the speed of moving electrons in the nth orbit.

The relation between vand rn is

Vn = \(\frac{e}{4\Pi \epsilon _{0}mr_{n}}\)

Substituting the value of  Vfrom equation 1 in the above equation  and solving for r we get,

\( r = \frac{n^{2}h^{2}}{4\Pi ^{2}me^{2}} * \frac{1}{z}\) \( \Rightarrow 0.529 * \frac{n^{2}}{z} Å \)

Angstroms, where n= principal quantum number of orbit and Z= atomic number.

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