A $10 - \mathrm { g }$ bouncy ball is confined in a $8.3 - \mathrm { cm }$-long box. What is its minimum energy? $( h = 6.626 \times$ $10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )
A) $3.2 \times 10 ^ { - 46 } \mathrm {~J}$
B) $8.1 \times 10 ^ { - 65 } \mathrm {~J}$
C) $9.4 \times 10 ^ { - 75 } \mathrm {~J}$
D) $1.3 \times 10 ^ { - 20 } \mathrm {~J}$

Question

Quizplus · Accepted Answer

The minimum energy of a particle in a box is given by the quantum mechanical formula $E = \frac{h^2}{8mL^2}$. Substituting the given values (mass $m = 10 \, \text{g} = 0.01 \, \text{kg}$, length $L = 8.3 \, \text{cm} = 0.083 \, \text{m}$), the calculation yields approximately $8.1 \times 10^{-65} \, \text{J}$.

A 10−g10 - \mathrm { g }10−g Bouncy Ball Is Confined in A

A $10 - \mathrm { g }$ Bouncy Ball Is Confined in A