How much energy would be required to excite one mole of hydrogen atoms from their ground state to n₂ = 10?

Question

Quizplus · Accepted Answer

The energy required to excite one mole of hydrogen atoms from their ground state to a specified excited state can be calculated using the Rydberg formula for hydrogen. The energy difference (ΔE) for transitions in hydrogen is given by ΔE = R_H * (1/n1^2 - 1/n2^2), where R_H is the Rydberg constant for hydrogen (approximately 2.18 × 10^-18 J), n1 is the principal quantum number of the initial state (1 for the ground state), and n2 is the principal quantum number of the final state. For a transition to n=10, ΔE per atom = 2.18 × 10^-18 J * (1/1^2 - 1/10^2). To find the energy per mole, this value is multiplied by Avogadro's number (approximately 6.022 × 10^23 mol^-1), resulting in an energy requirement on the order of 10^16 J/mol, which matches the magnitude in choice B.

How Much Energy Would Be Required to Excite One Mole