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because the proton feels no forcebecause the proton is more massivebecause the p

ID: 1589913 • Letter: B

Question

because the proton feels no forcebecause the proton is more massivebecause the proton is the nucleus

In the "Bohr model" of the Hydrogen atom, a single electron is said to have a circular orbit around the nucleus (in this case consisting of a single proton), analogously to how the Earth orbits the Sun. If the electron orbits at a distance of 0.5.1010 m Sun. If the electron orbits at a distance of 0.5-10-10 m Electron Proton a.) What is the electric force felt by the electron? b.) What speed must the electron have in order to maintain its orbit? m/s mi/hr c.) Why does the electron orbit around the proton (instead of vice versa)? (Select all that apply.) because the proton feels no force because the proton is more massive because the proton is the nucleus

Explanation / Answer

(a)   For the electric force felt by the electron,

Let, q_p = the charge of the proton = 1.602*10^-19 C

q_e = the charge of the electron = -1.602*10^-19 C

r = the radius of the orbit = 5*10^-11 m

k = 8.9*10^9 N•m²/C²

The electric force from the proton to the electron where a negative value indicates attraction,

F_e = k(q_p)(q_e) / r^2 = 8.9*10^9(1.602*10^-19)(-1.602*10^-19) / (5*10^-11)^2 = 9.136*10^-6 N

(b) For the speed must the electron have in order to maintain its orbit:

m = the mass of the electron = 9.1*10^-31 kg

Let, V = the tangential velocity of the electron

and F_c = the centripetal force of the electron = m(V^2) / r

In a circular orbit, F_c = F_e

=> m(V^2) / r = k(q_p)(q_e) / r^2

=>   m(V^2) = k(q_p)(q_e) / r

=>   V^2 = k(q_p)(q_e) / {(m)r}

=> V = [k(q_p)(q_e) / {(m)r}]

      = [8.9*10^9(1.602*10^-19)(1.602*10^-19) / { (9.1*10^-31)*5*10^-11}]

=>   V = 2.24*10^8 m/s = 5.01*10^8 mi / hr

(c)   The correct option could be:

---> (b) because the proton is more massive