Question

III. (12 pts) The electron of a hydrogen atom is excited to the n= 5 state. (a) what is the Bohr radius of the electron? (b) what is the total energy of the electron? (c) what is the electron's Coulomb potential energy and kinetic energy?

Answer 1

(a) 13.225 A

(b) -0. 54eV

(c) K. E. = 0.54eV

P. E. = -1. 08eV

Sol Given, H-atom sie z = 1 (a) Bohr radius of e- is given by et R = 0.529 n² 20:529_(5) 13.225_A r مد (6) Total energy of e- is given by En = - 13.6 7² eV n2 13.6 (514 0.540 eV -E (7 é Coulomb pot energy , & K. E for e e- to move in circular orbit, the Colomb face must equal to centripetal folle k qe muz r r² muz ku (i) Now, Kinetic K.E energy is - L muz 2 {using to} 2 1 (k s for r use (a) WWWMWWWWWWWWWWW

+ od 9x10x (1.68101932 13.-22.5x10 to 9x10 x 2.5681038 13.225x10-10 а -29 0.87 X 10 J -0.87X Lot 1.6 X 10-19 I ev 0.54 ev KE - & Potential energy -q v = q (kq) U = r -kq² r GX10 x (1.6810193 13.225 X 100 1.74 x 10-19 I 1.7481019 ev 1.6x10 4.08 eV IPE Қ. Е P.E. = -1.08 eV el 9 Т.Е. K. E + P.E. 0.54 1.08 0.54 ev (which is (6)