Final answer:
The mass of the hydrogen-line atom is 1.66 x 10^-27 kg. The magnitude of the lowest state energy is -13.6 eV. The shortest wavelength is approximately 4 x 10^-12 m.
Step-by-step explanation:
In order to calculate the mass of the hydrogen-line atom, we need to know the charge of the particle. Assuming it is a hydrogen atom, the charge would be +1. The mass of a hydrogen atom is approximately 1 atomic mass unit, which is equivalent to 1.66 x 10^-27 kg. Therefore, the mass of this particle would be the same, 1.66 x 10^-27 kg.
To calculate the magnitude of the lowest state energy, we can use the formula E = -13.6 eV / n^2, where n is the principal quantum number. For the lowest state (n = 1), the energy would be -13.6 eV.
The shortest wavelength can be calculated using the formula λ = 2πr, where r is the Bohr radius. In this case, the Bohr radius is given as 0.002 nm, which is equivalent to 2 x 10^-12 m. Therefore, the shortest wavelength would be approximately 4 x 10^-12 m.