Question

For the Bohr's quantization I need the solution for the whole question but for the second question I just need part (iii) but I posted the whole question because it is all connected.

(c) Bohr's quantization conditions for the allowed state of an electron in the hy- drogen atom are given by h Ln=mvaIn= "2T where n 1,2, 3.. Consider a ten-fold ionized sodium ion, Na10+, which is obtained by removing ten electrons from a Na atom (Z = 11). (i) Derive the radii (rn) and the speeds (v) of the allowed states (ii) Calculate the orbiting speed and orbital angular momentum of the electron when the ion is in its third excited state

Answer 1

Qushen Ln aTT elechn mouin Centpehal forae nuclонs anoumd orbi mu2 (in Coulom b farce ach'ng electon Orbit Пе2 4-T12 oro povida centnpeta faa b elochon anound Coulomb nuclaus in cirular orbits. move le2 m 2 le2 2 from equah'en D n h mn Tn TT n h = "6n 2 TT2 m2n h2h2 use in equg h'on le 2- 2 4п2 m2 4Tm n2 h2o in equahon ex prersion f this we {1e2 nh_ Vn = TTm (T me2 и з46

for electon im excited tahe thind .exi519)2 Ile 2 8x 6-62 6X (o 3+x 8-8Sxlo12 o. o6 o 27X lo m/s 94 m/s n h -39- 4X 6 626 Y (O - 34- 4 22o 3x 10 m2/s atom enngy nih lavel i given z2 RE n2 has ground state in bombarded gan eloctons aw hen 3-2 2e V Whan fumd we to excited izht So only mono chormahi -2RE EntE n; +1 T hi)2 3.82eV mi+1)2 4 93eV Now fom tansihon wi be poraible hitl) state Hhar then and mit2) Atate 4.93 ev is As 4 93eV So ni G2lole neadeal

Now 22 RE Eni+2- En mith2 it22 -L 387리 i+22 n2 - 22RE 22R 2 2 + mitz)2 49 3e 22RE) Ent2- Enit1 4.93eV 3 82 eV

enegy lewl düagram So 4.93e V nit 3-82eV tate