The electron in a helium ion moves from a Bohr's orbit whose principal quantum number is 4 to another whose quantum number is 6.calculate the energy of transition in this process.
E = 2.18E-18*Z^2(1/16 - 1/36)
Note this goes from 4 to 6 so energy must be absorbed.
To calculate the energy of the transition, we need to use the equation:
ΔE = E_final - E_initial
where ΔE is the energy of the transition, E_final is the energy of the final state, and E_initial is the energy of the initial state.
In atomic physics, the energy of an electron in a hydrogen-like ion (such as helium) can be calculated using the following equation:
E_n = -13.6 eV / n^2
where E_n is the energy of the electron in the nth energy level (orbit) and n is the principal quantum number.
Given that the electron moves from an orbit with n = 4 (initial state) to an orbit with n = 6 (final state), we can substitute these values into the equation:
E_final = -13.6 eV / (6^2)
E_initial = -13.6 eV / (4^2)
E_final = -13.6 eV / 36
E_initial = -13.6 eV / 16
Now we can calculate the energy of the transition:
ΔE = E_final - E_initial
ΔE = (-13.6 eV / 36) - (-13.6 eV / 16)
ΔE = -13.6 eV * (1/36 - 1/16)
Simplifying the equation:
ΔE = -13.6 eV * (4 - 9)/(36 * 16)
ΔE = -13.6 eV * (-5/576)
ΔE = (13.6 * 5) / 576 eV
ΔE = 0.118 eV (rounded to three decimal places)
Therefore, the energy of the transition in this process is approximately 0.118 electron volts (eV).