Open Question
An electron in a hydrogen atom is excited with electrical energy to an excited state with n = 2. The atom then emits a photon. What is the value of n for the electron after the emission?
9. Quantum Mechanics
Bohr Model
Multiple Choice
According to the Bohr theory of the hydrogen atom, what is the minimum energy (in J) needed to ionize a hydrogen atom from the n=2 state?
A
1.64 x 10^-18 J
B
2.18 x 10^-18 J
C
3.03 x 10^-19 J
D
5.45 x 10^-19 J
Verified step by step guidance1
Understand that ionization energy is the energy required to remove an electron completely from an atom. For hydrogen, this involves moving the electron from its current energy level to infinity.
Recall the Bohr model formula for the energy of an electron in a hydrogen atom: , where is the Rydberg constant (approximately J) and is the principal quantum number.
Calculate the energy of the electron in the n=2 state using the formula: .
Recognize that the energy needed to ionize the atom from the n=2 state is the difference between the energy at n=2 and the energy at n=infinity (which is 0). Therefore, the ionization energy is simply the absolute value of the energy calculated for n=2.
Compare the calculated ionization energy with the given options to identify the correct answer.
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