Final Answer:
The energy change when one mole of electrons in a sample of hydrogen atoms transitions from n = 6 to n = 3 is approximately -328.73 kJ/mol.
Step-by-step explanation:
The energy change in a hydrogen atom as an electron transitions between energy levels can be calculated using the Rydberg formula: ΔE = -2.178 × 10^(-18) J * (1/n_f^2 - 1/n_i^2), where ΔE is the energy change, n_f is the final energy level, and n_i is the initial energy level. To convert the energy from joules to kilojoules, we divide by 1000.
In this case, when transitioning from n = 6 to n = 3, the calculation is as follows:
ΔE = -2.178 × 10^(-18) J * (1/3^2 - 1/6^2)
ΔE ≈ -2.178 × 10^(-18) J * (1/9 - 1/36)
ΔE ≈ -2.178 × 10^(-18) J * (4/36 - 1/36)
ΔE ≈ -2.178 × 10^(-18) J * (3/36)
ΔE ≈ -2.178 × 10^(-18) J * (1/12)
ΔE ≈ -1.815 × 10^(-19) J
To convert this energy change to kilojoules, we divide by 1000:
ΔE ≈ -1.815 × 10^(-19) J / 1000 kJ/J
ΔE ≈ -1.815 × 10^(-22) kJ
Therefore, the energy change is approximately -1.815 × 10^(-22) kJ.