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Suppose the electron in a hydrogen atom is modeled as an electron in a one-dimensional box...

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Physics

Suppose the electron in a hydrogen atom is modeled as anelectron in a one-dimensional box of length equal to the Bohrdiameter, 2a0. What would be the ground-stateenergy of this \"atom\"?
______________eV

Answer & Explanation Solved by verified expert
4.0 Ratings (761 Votes)

With the following data:

  • Length of the box : L = 2 a o  
  • a o is bohr radius -- 0.0529 nm --   

Allowed energy of a particle in one dimensional box is

               E n = n 2 h 2 / 8 m L 2     

Where   m is mass electron and h is plancks constant

Ground state energy of the atom is:

           E =   h 2 / 8 m L 2    

               = ( 6.635 *10 -34 Js ) 2 / ( 8)(9.11*10-31 kg ) ( 2*0.0529 *10-9 ) 2  

               =  53.963*10-19 J

               = 33.7273 eV

Actual ground state energy of hydrogen atom is: -13.6 eV

Diving:

              33.7273 / 13.6   = 2.4799 times
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