According to the Bohr theory of the hydrogen atom, the minimum energy (in J) needed to ionize a hydrogen atom from the n = 2 state is A) 2.18 * 10¯¹⁸ J B) 1.64 * 10¯¹⁸ J C) 5.45 *10¯¹⁹ J D) 3.03 * 10¯¹⁹ J E) None of these choices is correct.

Question

Quizplus · Accepted Answer

According to the Bohr theory, the energy of an electron in the nth energy level of a hydrogen atom is given by:
En = - (2.18 × 10^-18 J) / n^2
Here, n = 2 for the initial energy level of the hydrogen atom.

The energy required to ionize the hydrogen atom from the n = 2 state is equal to the difference between the energy levels of the initial (n = 2) and final (n = infinity) states:
ΔE = E(infinity) - E(2) = - (2.18 × 10^-18 J) / infinity^2 + (2.18 × 10^-18 J) / 2^2

ΔE = (2.18 × 10^-18 J) / 4

ΔE = 5.45 × 10^-19 J

Therefore, the minimum energy required to ionize a hydrogen atom from the n = 2 state is 5.45 × 10^-19 J, which corresponds to answer choice C.

According to the Bohr Theory of the Hydrogen Atom, the Minimum