Question

Do the wave lengths which you observed vary with the radii of the stable orbits? If so, how and why.

p.s: It did vary, im not sure why though

Answer 1

Energy of a orbit is inversely proportional to radius.

E = -Ze^2/ 8*o * r

Also E = hc/

So, wavelength and radius are directly proportional. If radius of the orbit increases, energy increases. This is because, potential energy of the orbit decreases as two bodies (in this case a nucleus and a electron) are moved further.

The kinetic energy, however, increases as you increase. This is because the centripetal force of attraction is less and so the centripetal acceleration is also less and the orbital velocity is less. You can easily do this calculation from first principles. Between the two, the (negative) potential energy (measured relative to infinite distance) has twice the magnitude of the (positive) kinetic energy, so the former dominates.

A decrease in energy is increase in wavelength. Hence the observation.