28. The strength of the electrostatic force between two charges q and q2 sepa- r

Question

28. The strength of the electrostatic force between two charges q and q2 sepa- rated by a distance r is given by F kc1q2/r2, where kc is a constant given (a) What is the electrostatic force between an electron and a proton separated (b) If this same amount of force were due to a spring stretched by 0.05 nm, by 8.99 x 10 Nm2/C2 by 0.05 nm, as is typical in an atom? what would be the force constant for this spring? (F =-Kx, where K IS the force constant.) (c) Suppose that an electron were connected to a proton by a spring with force constant equal to that which you calculated in part (b). What would be the angular frequency (co2-k/m) for the electron's oscillations? d) What would be the separation between allowed energy levels, in ev? (e) How does this compare with the 10.2 eV separation between the ground state and the first excited state in hydrogen?

Explanation / Answer

28.

a)

q = magnitude of charge on electron and proton = 1.6 x 10-19 C

r = distance between electron and proton = 0.05 x 10-9 m

electrostatic force is given as

F = k q2/r2

F = (8.99 x 109) (1.6 x 10-19)2/(0.05 x 10-9)2

F = 9.2 x 10-8 N

b)

k = spring constant

x = stretch in the spring = 0.05 x 10-9 m

Spring force is given as

Fs = k x

Since

Fs = F

kx = 9.2 x 10-8

k (0.05 x 10-9) = 9.2 x 10-8

k = 1849 N/m

c)

m = mass of electron = 9.1 x 10-31 kg

angular frequency is given as

w = sqrt(k/m) = sqrt(1849/(9.1 x 10-31)) = 4.5 x 1016

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