A photon of energy 12.75eV is completely absorbed by a hydrogen aton i...
Answer:
Introduction:
When a photon of energy is absorbed by a hydrogen atom in ground state, it excites the electron to a higher energy level. The energy of the photon must be equal to the difference in energy between the ground state and the excited state.
Calculation:
The energy required to excite a hydrogen atom from its ground state to the first excited state is 10.2 eV. Therefore, if a photon with energy greater than 10.2 eV is absorbed by a hydrogen atom in its ground state, the electron will be excited to a higher energy level.
The energy of the photon is given as 12.75 eV. This energy is greater than the energy required to excite the electron to the first excited state. Therefore, the electron will be excited to the first excited state.
The energy difference between the ground state and the first excited state is given by the equation:
ΔE = E2 - E1
Where,
ΔE = Energy difference
E2 = Energy of the excited state
E1 = Energy of the ground state
Substituting the values, we get:
ΔE = -10.2 eV - (-13.6 eV)
ΔE = 3.4 eV
Therefore, the principle quantum number of the excited state is 2.
Conclusion:
The photon of energy 12.75 eV is completely absorbed by a hydrogen atom initially in ground state, and the principle quantum number of the excited state is 2.