Laser Energy Release Calculation
This solution details the calculation for the energy released during a single laser pulse in a two-level atomic system.
Given Parameters
- Energy separation between levels: $\Delta E = 2$ eV
- Number of atoms in ground state: $N_g = 4 \times 10^{20}$
- Number of atoms in excited state: $N_e = 7 \times 10^{20}$
Energy Release Calculation
The total energy released ($E$) is determined by the number of atoms transitioning and the energy difference ($\Delta E$) per atom. The calculation uses the following formula:
$ E = \frac{N_e - N_g}{2} \times \Delta E $
This formula considers half the population inversion multiplied by the energy separation.
Step-by-Step Calculation
- Determine the population inversion: $N_{inv} = N_e - N_g = 7 \times 10^{20} - 4 \times 10^{20} = 3 \times 10^{20}$ atoms.
- Calculate the effective number of atoms contributing to energy release: $N_{eff} = \frac{N_{inv}}{2} = \frac{3 \times 10^{20}}{2} = 1.5 \times 10^{20}$ atoms.
- Calculate the total energy released in electron volts (eV): $E_{eV} = N_{eff} \times \Delta E = (1.5 \times 10^{20} \text{ atoms}) \times (2 \text{ eV/atom}) = 3 \times 10^{20}$ eV.
- Convert the total energy from eV to Joules (J). Use the conversion factor $1 \text{ eV} = 1.602 \times 10^{-19}$ J: $E_J = (3 \times 10^{20}) \times (1.602 \times 10^{-19})$ J $E_J = 4.806 \times 10^1$ J $E_J = 48.06$ J.
Final Result
The calculated energy release is approximately 48.06 J. This value rounds to 48 J.
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