I have part a.), but after that its all not really working out for me. If you co

Question

I have part a.), but after that its all not really working out for me. If you could show all of your steps with the final answer that would be lovely. thank you!!


A hydrogen atom is in its second excited state (n = 3). Using the Bohr theory of the atom, calculate the following.

(a) the radius of the orbit
ANSWER = .4761 nm

(b) the linear momentum of the electron
? kg·m/s

(c) the angular momentum of the electron
? J·s

(d) the kinetic energy
? eV

(e) the potential energy
? eV

(f) the total energy
? eV

thank you so much in advance.!!

Explanation / Answer

b) L = n = mvr, so

mv = p = n/r = 3(1.055*10^-34 Js)/(0.4761 * 10^-9 m) = 6.65*10^-25 Ns

c) L = n = 3(1.055*10^-34 Js) = 3.16*10^-34 Js

d) v = p/m = (6.65*10^-25 Ns)/(9.11*10^-31 kg) = 7.3*10^5 m/s, so

K = (1/2)mv^2 = (1/2)(9.11*10^-31 kg)(7.3*10^5 m/s)^2 = 2.43*10^-19 J * 1 eV/ 1.602*10^-19 J = 1.52 eV

e) U = kq1q2/r = (9*10^9 Nm^2/C^2)(1.602*10^-19 C)^2 / (0.4761 *10^-9 m) = 4.85*10^-19 J = 3.03 eV

f) E = K + U = 1.52 eV + 3.03 eV = 4.55eV

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