Final answer:
Atoms can be ionized by thermal collisions at high temperatures like those found in the solar corona; C⁺⁵ ion energies are 36 times greater than those of hydrogen, and the wavelength of the first line in the Paschen series can be calculated using the Rydberg formula adjusted for the atomic number of Carbon.
The correct answer is options a) True.
Step-by-step explanation:
Atoms can indeed be ionized by thermal collisions in environments with high temperatures, such as the solar corona. A carbon atom that loses five of its electrons is denoted as C⁺⁵, leaving it with just a single electron, mimicking a hydrogen-like ion. This leads to a couple of interesting questions:
By what factor are the energies of its hydrogen-like levels greater than those of hydrogen?
What is the wavelength of the first line in this ion's Paschen series?
(a) The energy levels for a hydrogen-like ion can be determined using the formula En = -13.6 Z2/n2 eV, where Z is the atomic number of the ion and n is the principal quantum number. For a C⁺⁵ ion, Z=6. Therefore, the energy levels for C+5 will be (62) or 36 times greater than those of hydrogen.
(b) To find the wavelength of the first line in the Paschen series for C⁺⁵, we need to use the Rydberg formula for hydrogen-like ions, which can be adjusted for different atomic numbers. The Paschen series corresponds to transitions where the final energy level is n=3. The first line in this series would involve a transition from the next highest energy level, n=4, to n=3. The wavelength can be calculated using the modified Rydberg formula: 1/λ = R(Z2)(1/n12 - 1/n22), where R is the Rydberg constant, Z is the atomic number, and n1 and n2 are the principal quantum numbers. Using this formula, the wavelength can be determined for the C⁺⁵ ion.
The correct answer is options a) True.