Hydrogen atom in ground state is excited by a monochromatoc radiation ...
Hydrogen atom in ground state is excited by a monochromatoc radiation ...
Excitation of Hydrogen Atom:
- When a hydrogen atom in its ground state is excited by monochromatic radiation of wavelength 975 Angstrom, the electron moves to a higher energy level.
Spectral Lines in the Resulting Spectrum:
- The electron in the excited state will eventually transition back to the ground state, emitting photons in the process.
- The spectral lines in the resulting spectrum correspond to these emitted photons.
Calculation of Spectral Lines:
- The number of spectral lines emitted can be calculated using the formula:
\[ \Delta E = \dfrac{hc}{\lambda} \]
Where:
- ΔE is the energy difference between the initial and final states,
- h is the Planck's constant,
- c is the speed of light,
- λ is the wavelength of the absorbed radiation.
Energy Levels in Hydrogen Atom:
- In a hydrogen atom, the energy levels are given by the formula:
\[ E_n = -\dfrac{13.6}{n^2} \]
Where n is the quantum number representing the energy level.
Number of Spectral Lines:
- When the excited electron transitions back to the ground state (n=1), it can do so from different higher energy levels.
- The possible transitions are from n=3, n=4, n=5, n=6, n=7, and so on, down to n=2 and finally to n=1.
- Therefore, there are a total of 6 possible spectral lines in the resulting spectrum.
Thus, the correct answer is A) 6 spectral lines.
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