If the mass of the particle is m = 1.0 × 10⁻³⁰ kg and a = 6.6 nm, the energy of the particle in its ground state is closest to 0.8 meV, 8 meV, 80 meV, or 800 meV?

The situation is studied as a particle in a box problem. According to the model, energy in n'th state is given by

(n²h²)/(8ma²)

For the ground state, n=1. Substituting the given values:

= (1² × (6.626 × 10⁻³⁴)²) / (8 × 10⁻³⁰ × (6.6 × 10⁻⁹)²) × 1.6 × 10⁻¹⁹

= 8 meV