Calculating Energies in Box Potential

[Messy]

Homework Statement

Consider the box potential
V (x) = 0 0 < x < a
1 elsewhere

a) Estimate the energies of the ground state as well as those of the First and second
excited states for
i) an electron enclosed in a box of size a = 10E-10 m. Express your answer in
electron volts.
ii) a 1 g metallic sphere which is moving in box of size a = 10 cm. Express your
answer in joules.
b) Discuss the importance of quantum effects for both these two systems.

Homework Equations

E1 = ((h)^2 ) / ( 8 * m * L ^2)

En = n^2 * E1

The Attempt at a Solution

The First problem is , I am not sure about L(Length) . Is this equal to the size of the box 'a' in part i and ii.

The Second Problem is how can i define the importantance of quantum effect (b) .. I mean should i have to define with the varying size what change i am observing in Energy Levels .

 

[Messy]

May be i have to put this one in Advance Physics Sections :-)