Question

The lowest energy that a neutron can have if confined to move along the age of an impedance box of length 10^-14m is
1)3.29×10^-13 J
2)2.05×10^-8 J
3)1.16×10^-13 J
4)7.09×10^-10J

Answer 1

The particle energy takes on certain discrete values. It is usually said that a particle is in certain energy states.

$$E_n =\frac{n^2h^2}{8mL^2}$$

We have conditions

$$n=1; L=10^{-14} m=1.67 \cdot 10^{-27}$$ $$E_n =\frac{1^2\cdot 6.63*10^{-34}}{8\cdot 1.67 \cdot 10^{-27}\cdot 10^{-28}} =3.29 \cdot 10^{-13} (J)$$

Answer is 1) 3.29x10^-13 (J)