According to the Bohr theory, the energy required to ionize a hydrogen atom from the n = 2 state can be calculated using the formula:
E = (-13.6 eV) * (Z^2/n^2)
where E is the energy, Z is the atomic number (which is 1 for hydrogen), and n is the principal quantum number of the initial state.
To ionize the hydrogen atom from the n = 2 state, it needs to be excited to the ionization state (n = infinity). Therefore, the final value of n is infinity.
Substituting these values into the formula, we get:
E = (-13.6 eV) * (1^2/2^2 - 1/infinity^2)
E = (-13.6 eV) * (1/4 - 0)
E = (-13.6 eV) * (1/4)
E = -3.4 eV
To convert eV to Joules, we can use the conversion factor 1 eV = 1.602 x 10^-19 J. Therefore,
E = (-3.4 eV) * (1.602 x 10^-19 J/eV)
E = -5.446 x 10^-19 J
However, this energy value is negative because the electron is bound to the atom and the energy required to remove it is equivalent to the energy that is released when it is bound to the atom. So, the absolute value of this energy is the minimum energy required to ionize a hydrogen atom from the n = 2 state:
|E| = 5.446 x 10^-19 J
Therefore, the minimum energy required to ionize a hydrogen atom from the n = 2 state according to the Bohr theory is approximately 5.446 x 10^-19 J.