How stable is an atom? Recall from your mechanics class, that to keep a body, su

Question

How stable is an atom? Recall from your mechanics class, that to keep a body, such as a Low Earth Orbit (LEO) satellite, in orbit, it needs to be given a certain initial (tangential) velocity. Essentially this velocity will cause a centripetal force that counteracts the gravitation pull of the earth. Fora hydrogen atom, the average distance between the nucleus and the electron is about 5x10^-11 m. From Coulomb^?s law, calculate the speed at which the electron has to move to stay in a stable orbit around the nucleus. How does that speed compare to the speed of light? Hint: To get a stable orbit, the centripetal force pushing out should match the Coulomb force pushing in. The centripetal force is equal to Fcentripetal = mv^2/r

Explanation / Answer

speed of the electron in first orbit is

v = h/ 2 pi m r = 6.63 * 10 ^-34 JS/ 2 pi ( 9.10938356 × 10-31 kilograms) ( 5 * 10 ^-11 m) = 0.0231 * 10 ^8 m/s

compare speed of the electron with speed of light

v/c = 0.0231 * 10 ^8 m/s/ 3 * 10 ^8 m/s = 0.0077

v = c ( 0.0077)

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