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

Suppose the electron in a hydrogen atom is modeled as an electron in a one-dimensional box of length equal to the Bohr diameter, 2a₀. What would be the ground-state energy of this "atom"?
______________eV

Expert Solution

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

genius_generous answered 1 year ago

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