A laser emits 1.0 × 10¹⁹ photons per second from an excited state with energy E₂ = 1.17 eV. The lower energy level is E₁ = 0 eV. What is the wavelength of this laser?

Verified step by step guidance

1. Convert the energy difference between the two levels (E2 - E1) from electron volts (eV) to joules (J). Use the conversion factor: 1 eV = 1.602 × 10⁻¹⁹ J. The energy difference is ΔE = E2 - E1 = 1.17 eV.
2. Use the relationship between energy and wavelength given by the equation: E = h * c / λ, where E is the energy difference (in joules), h is Planck's constant (6.626 × 10⁻³⁴ J·s), c is the speed of light (3.00 × 10⁸ m/s), and λ is the wavelength (in meters). Rearrange the equation to solve for λ: λ = h * c / ΔE.
3. Substitute the values of h, c, and ΔE (converted to joules) into the equation to calculate the wavelength λ.
4. Convert the wavelength from meters to nanometers (1 m = 10⁹ nm) for a more convenient unit, if needed.
5. Verify the units and ensure the final wavelength is consistent with the expected range for laser emissions, typically in the visible or near-visible spectrum.

Key Concepts

Photon Energy

The energy of a photon is directly related to its frequency and inversely related to its wavelength. It can be calculated using the equation E = hν, where E is the energy, h is Planck's constant (6.626 × 10^-34 J·s), and ν is the frequency. In this context, the energy difference between the excited state and the lower energy level determines the energy of the emitted photons.

Wavelength Calculation

The wavelength of a photon can be determined using the relationship between energy and wavelength, given by the equation λ = hc/E, where λ is the wavelength, h is Planck's constant, c is the speed of light (approximately 3.00 × 10^8 m/s), and E is the energy of the photon. This formula allows us to convert the energy of the emitted photons into their corresponding wavelength.

Laser Emission

A laser emits light through a process called stimulated emission, where photons stimulate excited atoms to emit additional photons of the same energy, phase, and direction. The number of photons emitted per second indicates the intensity of the laser, and in this case, it is essential to understand how the energy levels of the atoms relate to the characteristics of the emitted light.