energy of nth level is given as
where h=planck's constant
m=mass of the particle
L=box length=1 nm
as mass is not provided,using values of all other symbols,
energy of nth level=1.372*10^(-30)*n^2/m eV
part a:
difference of energy between n=1 and n=2 is given by
(1.372*10^(-30)*2^2/m )-(1.372*10^(-30)*1^2/m )
=4.116*10^(-30)/m eV
part b:
energy sepration between n=8 and n=9 is given by
(1.372*10^(-30)*9^2/m )-(1.372*10^(-30)*8^2/m )
=2.3324*10^(-29)/m eV
part c:
as n increases, energy sepration=(1.372*10^(-30)*(n+1)^2/m )-(1.372*10^(-30)*n^2/m )
=(1.372*10^(-30)/m)*(n^2+2*n+1-n^2)
=(1.372*10^(-30)/m)*(2*n+1)
so as n increases, the energy sepration increases.
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note: use the value of m for the mass of the particle to get particular answers.
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