A particle of mass \(m = 5.0 \times 10^{-31}\) kg is confined in a one-dimensional box of length \(L = 3.0 \times 10^{-10}\) m. Calculate the energy difference between the first excited state \(( n = 2 )\) and the ground state \(( n = 1 )\).
1
\(2.05 \times 10^{-18} J\)
2
\( 6.22 \times 10^{-19} J\)
3
\( 4.55 \times 10^{-19} J\)
4
\( 3.66 \times 10^{-18} J\)