Question

| The principle quantum number n characterizes the electronic interactions between the electron and the nucleus of an H-atom. (5 points) 1. Calculate the longest wavelength absorption (in nm) of the electron at the ground state. 2. Calculate the energy difference between the ground state and the 1st excited state. 3. Calculate the ratio of the probability of finding the electron at the first excited state over that at the ground state at 25°C. 4. Calculate the ratio of the probability of finding the electron at the first excited state over that at the ground state at 1000K.

Answer 1

If
ē in the nth orbit is PERRESENTED of AN THE WAVE NUMBER by u. FOR A TRANSITION 5) o= 109677 aro (t 만 where n₂ = DESTINATION ORBIT ORIGIN ORBIT ni 5) 22 la 109677am (1 ( BECAUSE LONGEST WAVE LENGTH IMPUES SHORTEST ENERY SHORTEST WAVE NUMBER AND SO THE

- 109677 annil (+-+) (a) a 109 677 en = 82 257.75 km [for EMISSION (): WAVE LENGTH 13 19 IT 1.2156 xios =) = 1 -7 1.2156 X10 mmc 0.0121 nom (for ABSORATION THE ABOVE IS THE CONGEST WAVELENGTH THAT must BE ABSORDED AND IS FROM A TRANSITION n= ln-2 IT 2 GROUND STATE; nel ETCHED FIRST STATE; n=2 in: PRINCIPAL QUANTUM NUMBER E = -2: 18 x1018 (txt) (7-6) -2.18 x 1518 । - 18 = -1.635x10 ОР AS E AMOUNT ENERGY MUST BE MITTED TO REACH GROUND SATE from n=2 (FIRST FAUTED STATE) THE ENERUM DIFFERENCE B/W THE Two most hour F = -10634x1018 J.

ONE PROBABILITY OR FINDING A мро и мом 10 OP DATE FUTED STATES COMPARED TO GROUND STATE Plea) plsio E (32) /kr e-t(s)/kr denna shol (2+1)=62. DEGENERALY OF ENERGY LEVELS -p ENERU Ezi THERE ARE "Y' STATES with PLE) 46-(tz-El)/KT PLE 10. 20v | г 7= 2° с Че - 29 $ 54 24° па8 : Is L. — 10 lev/8-66x1055 248 , че (less than 10 17 ) HENLE You will NEVER FIND р мрточEN MUM IN Поом TEMPEN) vu « PKцу Есит) SyMK (4) wOW EVER AT 10ook. P (E) 4--0-2-v/ e thos 5 x 100 х PLED с 10-lev(о: 08 66 2a e 2 - 81 10 5) eLog 1uTM AND YOU HAVE A LARUER THIS 13 THE RAT LO Нpsy -хито A ию очем мом ) 1 Of FINDING looor SMu
you've any related questions mate,do comment.

Cheers .