Question

1 4.76/14.28 points | Previous Answers ZinPhysLS3 19.P.002. A hydrogen atom is in its third excited state (n = 4). Using Bohr's atomic model, calculate the following. (a) the radius of the electron's orbit (in nm) 0.846 nm (b) the potential energy (in eV) of the electron -4.98 x ev (c) the total energy (in eV) of the electron x ev -4.21

Answer 1

A hydrogen atom in its third excited state n = 4 Radius of the orbit r_n = n^2 a_o = (4) ^2 (5.29 times 10^-11 m) = 0.846 times 10^-9 m = 0.846 nm (b) Potential energy P.E = -me^4/4n^2h^2 epsilon_o^2 = -(9 times 10^-31 kg) (1.6 times 10^-19 c) ^4/4 times (4) ^2(8.85 times 10^-12) ^2(6.625 times 10^-34) ^2 = -2.71 times 10^-19 J = -1.69 ev (c) Total energy (TE) = 0.847 ev + (-1.69 ev) = -0.846 ev