Consider the infinite square well of width a. V(x) is infinite out side well and

Question

Consider the infinite square well of width a. V(x) is infinite out side well and zero inside.

(a) Estimate the energies of the ground state
as well as those of the first and the second
excited states for (i) an electron enclosed in a
well of size a = 10^-10 m (express your answer
in electron volts); (ii) a 1g metallic sphere
which is moving in a well of size a = 10 cm
(express your answer in joules).
(b) Discuss the importance of the quantum
effects for both of these systems.
(c) Use the uncertainty principle to estimate
the velocities of the electron and the metallic
sphere.

Explanation / Answer

En = n2h2/8ma2 ;

for n=1;

E1 = h2 /8m(10-10)2 =( 6.624*10-34)2/8*9.1*10-34-20 = 6.027*10-15 J;

E2 = 22* E1 = 4*6.027*10-15 J = 24.108*10-15J;

using same formula , one can determine for metallic sphere ..

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