Atomic Structure

Using the Rydberg formula for electronic transitions.
The wavelength of emitted photon during transition is given by: Since the electron jumps to the first excited state, , so the equation becomes: Rearranging to solve for : Taking square root,

Step 1: Use the Relationship Between Energy and Potential Energy The electrostatic potential energy is related to the total energy by: For hydrogen-like atoms: Since given eV: Step 2: Solve for Step 3: Compute Electron Speed The speed of an electron in an orbit is given by: Thus, the correct answer is . \bigskip

The energy of a photon emitted during a transition from energy level to in a hydrogen atom is given by: $ n=2 n=1 E_1 = 13.6 \left( \frac{1}{1^2} - \frac{1}{2^2} \right) = 13.6 \times \frac{3}{4} = 10.2 \, \text{eV} n=5 n=2 E_2 = 13.6 \left( \frac{1}{2^2} - \frac{1}{5^2} \right) = 13.6 \times \frac{21}{100} = 2.856 \, \text{eV} $