Final answer:
Using the energy-level formula for hydrogen atoms, the highest energy level to which a hydrogen atom can be excited by a 12.75 eV electron beam is determined to be n = 3. This is calculated by equating the energy of the beam to the energy difference required to move an electron between the ground state and an excited state.
"the correct option is approximately option C"
Step-by-step explanation:
The question involves determining the highest energy level that a hydrogen atom can be excited to when it is subjected to a 12.75 eV electron beam. This entails using the energy-level formula for a hydrogen atom which is given by En = -13.6 eV / n^2, where En is the energy of the nth level in electron volts and n is the principal quantum number. Hydrogen's ground state energy level (n=1) is -13.6 eV, and energy levels for excited states (n>1) are higher (closer to zero).
To find the highest energy level to which the hydrogen atom will be excited, we find the value of n when the energy equals 12.75 eV (the energy of the electron beam).
We set up the equation 12.75 eV = -(-13.6 eV) / n^2, and calculate the value of n. We find that n is closest to an integer when n = 3. Therefore, n = 3 is the highest energy level to which the hydrogen atom will be excited with an electron beam of energy 12.75 eV.