A hydrogen atom is excited from a state with n=1 to one withn=4. (a) Calculate t

Question

A hydrogen atom is excited from a state with n=1 to one withn=4. (a) Calculate the energy that must be absorbed by theatom. (b) Calculate and display on an energy-level diagram thedifferent photon energies that may be emitted if the atom returnsto its n=1 state. (c) Calculate the recoil speed of the hydrogen atom, assumedinitially at rest, if it makes the transition from n=4 to n=1 in asingle quantum jump. A hydrogen atom is excited from a state with n=1 to one withn=4. (a) Calculate the energy that must be absorbed by theatom. (b) Calculate and display on an energy-level diagram thedifferent photon energies that may be emitted if the atom returnsto its n=1 state. (c) Calculate the recoil speed of the hydrogen atom, assumedinitially at rest, if it makes the transition from n=4 to n=1 in asingle quantum jump.

Explanation / Answer

   for a hydrogen system..the energy is giveby....    E = 10978cm^-1 [ 1/1^2 - 1/4^2 ]......frmthe formula k[1/N(i)^2 - 1/N(f)^2]       now the second part suggests tha ........electronjumps to various levels with same probability....    so probable transitions are................4 to 3,, 4 to 2 ...4 to 1 ........    now energy of transition for 4 to 1...will besame as energy absorbed.....given above by E....    similarly...others can be found....    
thirs part can be kown by conservingenergy................    E = 1/2 Mass of electron x Vel^2    from above we get....vel................    by momentum conservation.....................Masselecron x vel of emission = Mass hydrogen x vel of recoil....        hope u calculate.......coz it istedious!!

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