To find the kinetic energy acquired by the atom during the transition from n = 5 to n = 2 in a hydrogen atom, we can use the energy conservation principle. The energy change is equal to the energy of the emitted photon, which is given by the difference in energy levels between the initial and final states.
The energy difference between two energy levels in a hydrogen atom is given by the formula:
ΔE = E_final - E_initial = -13.6 eV × [1/n_final^2 - 1/n_initial^2]
Substituting n_final = 2 and n_initial = 5 into the equation, we get:
ΔE = -13.6 eV × [1/2^2 - 1/5^2]
ΔE = -13.6 eV × (1/4 - 1/25)
ΔE = -13.6 eV × (25/100 - 4/100)
ΔE = -13.6 eV × (21/100)
ΔE = -13.6 eV × 0.21
ΔE = -2.856 eV
To convert the energy change to kinetic energy, we need to consider that the energy of the emitted photon is equal to the kinetic energy acquired by the atom. Thus, the kinetic energy acquired by the atom during the transition is 2.856 eV.
To convert the kinetic energy to microelectron volts (μeV), we can use the conversion factor 1 eV = 10^6 μeV:
Kinetic energy (in μeV) = 2.856 eV × 10^6 μeV/eV
Kinetic energy = 2.856 × 10^6 μeV
Therefore, the kinetic energy acquired by the atom due to the transition is approximately 2.856 × 10^6 μeV.