Calculate the classical frequency for the light emitted by an atom. To do so, note that the frequency of revolution is v/2pir, where r is the Bohr radius. Show that as n approches infinity in

f= 2pi2mk2e4/h3 times 2n-1/(n-a)2 n2

the expression varies as 1/n3 and reduces to the classical frequency.

Solution Preview

Because, classical frequency for the light emitted by an atom is given by the Bohr's formula for an electron jumps from nth level to mth level (n > m),
f = {m*Z^2*e^4/(8*ep^2*h^3)}*(1/n^2 - 1/m^2)
Here, ep = epsilon zero = permittivity of free space.

For, Z = 1 (Hydrogen atom),
f = {m*e^4/(8*ep^2*h^3)}*(1/n^2 - 1/m^2) ...(1)
This formula can be derived as:
Energy of an electron in an orbit of radius r,
E(r) = U + K
U = electrostatic potential energy due to attraction towards nucleus with Z nucleons,
U = -k*Z*e*e/r = -k*Z*e^2/r ......(2)
where, ...

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