Answer:
[tex]l=3.5*10^{-10}m[/tex]
Explanation:
From the question we are told that:
1st Energy [tex]E_1=12eV=4(3eV)[/tex]
2nd Energy [tex]E_2=27eV=9(3eV)[/tex]
3rd Energy [tex]E_3=48eV=16(3eV)[/tex]
Generally the equation for Energy E for electron in one dimensional box at ground state [tex]E_0[/tex] is mathematically given by
[tex]E_0=\frac{h}{8ml^2}[/tex]
[tex]E_0=\frac{h}{8ml^2}[/tex]
Therefore Length a is mathematically given as
[tex]l=\sqrt{\frac{h^2}{8mE_0} }[/tex]
[tex]l=\sqrt{\frac{(6.625*10^{-34})^2}{8(9.1*19^{-31}{(3eV(1.6*10^{-19}))}}[/tex]
[tex]l=3.5*10^{-10}m[/tex]
