Concept: In the Bohr model, the total energy of an electron in a given orbit is the sum of its kinetic and potential energies. By the Virial theorem for Coulombic forces, Kinetic Energy (\( K.E. \)) is exactly equal to the negative of the Total Energy (\( T.E. \)).
Formula:$$ K.E. = - T.E. $$
Solution:- The total energy of an electron in the first Bohr orbit (ground state, \( n=1 \)) of hydrogen is \( -13.6 \text{ eV} \).
- Kinetic energy is a scalar quantity of motion and must always be positive.
- Therefore, \( K.E. = -(-13.6 \text{ eV}) = +13.6 \text{ eV} \).
Why other options are incorrect:Option C (\( -13.6 \text{ eV} \)) represents the
Total Energy, not kinetic energy. Option A uses the wrong unit (Joules instead of electron-volts). Option D uses incorrect scaling (keV).
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