Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in th...
Explanation:
The given problem involves the excitation of hydrogen atoms by monochromatic radiation and the subsequent emission of spectral lines according to Bohr's theory. Let's analyze the process step by step.
Step 1: Ionization Potential of Hydrogen Atom
The ionization potential of a hydrogen atom is the energy required to remove an electron from the ground state of the atom. In this case, the ionization potential is given as 13.6 eV.
Step 2: Excitation of Hydrogen Atoms
The hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. This means that the incoming photons have an energy of 12.1 eV, and they are capable of exciting the hydrogen atoms.
Step 3: Bohr's Theory of Spectral Lines
According to Bohr's theory, when an electron in a hydrogen atom is excited to a higher energy level and then returns to a lower energy level, it emits a photon of specific energy. The energy of the emitted photon can be calculated using the formula:
E = E1 - E2
where E is the energy of the emitted photon, E1 is the energy of the higher energy level, and E2 is the energy of the lower energy level.
Step 4: Calculation of Spectral Lines
In this problem, the hydrogen atoms are excited from the ground state to a higher energy level by photons of energy 12.1 eV. The energy difference between the ground state and the excited state can be calculated as:
E = 13.6 eV - 12.1 eV = 1.5 eV
This means that when the excited hydrogen atoms return to the ground state, they will emit photons of energy 1.5 eV.
Now, let's consider the possible transitions that can occur when the excited hydrogen atoms return to the ground state:
1. Transition from the excited state to the ground state: This will result in the emission of a photon of energy 1.5 eV.
2. Transition from any higher energy level to the ground state: This will also result in the emission of a photon of energy 1.5 eV.
Therefore, there are multiple possible transitions that can occur, resulting in the emission of spectral lines. In this case, there are three possible transitions: one from the excited state to the ground state, and two from higher energy levels to the ground state.
Hence, the correct answer is option 'C', which states that three spectral lines will be emitted by the hydrogen atoms according to Bohr's theory.
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