Final answer:
The longest light wavelengths that can be used to ionize the lowest four energy levels of the hydrogen atom are found in the Lyman series. The wavelength of the energy quantum emitted in a downward transition from the first excited state of the atom to the ground state is approximately 121.6 nm.
Step-by-step explanation:
The longest light wavelengths that can be used to ionize the lowest four energy levels of the hydrogen atom are found in the Lyman series. The Lyman series includes photons with energies capable of exciting the electron from the ground state (energy level 1) to energy levels 2, 3, 4, and so on. The first five photons in the Lyman series have wavelengths of 121.6 nm, 102.6 nm, 97.3 nm, 95.0 nm, and 93.8 nm.
To find the wavelength of the energy quantum emitted in a downward transition from the first excited state of the atom (n=2) to the ground state (n=1), we can use the formula:
1/λ = R(1/n²₁ - 1/n²₂)
Plugging in the values for n₁=2 and n₂=1, where R is the Rydberg constant (approximately 1.097 × 10^7 m⁻¹), we can solve for λ. The wavelength of the energy quantum emitted in this transition is approximately 121.6 nm.