Bohr S Model For Hydrogen Atom

The energy of a photon emitted during a transition between two energy levels is given by the equation: where:
is the energy of the emitted radiation (in this case, ),
is Planck's constant,
is the frequency of the emitted radiation.
The frequency is related to the wavelength by the equation:
where:
is the speed of light,
is the wavelength of the emitted radiation.
Substitute into the energy equation:
Rearranging for :
Now, substitute the given values:
,
,
.
Thus:
Therefore, the wavelength of the radiation emitted is .

The energy of an electron in the hydrogen atom is given by the formula: Where is the principal quantum number. In the ground state, , so the energy of the electron in the ground state is: For the first excited state, , so the energy of the electron in the first excited state is: Now, the total energy consists of both kinetic energy and potential energy . According to the Virial Theorem: The total energy is: Since , it follows that , so . For the first excited state, we already know that . Therefore: And since : Thus, the kinetic energy is and the potential energy is . % Correct Answer Correct Answer:} (C) 3.4 eV, -6.8 eV