To determine the kinetic energy (K.E.) of an electron in the first excited state of a hydrogen atom, we need to understand the relationship between the total energy, potential energy, and kinetic energy in an atom. In a hydrogen atom, the total energy (E) of an electron in the nth state is given by:

Eₙ = −13.6/n² eV For the first excited state, n = 2.

So, plugging in the value: E₂ = −13.6/2² = −13.6/4 = −3.4 eV

This value represents the total energy (E) of the electron in the first excited state. According to the virial theorem for an electron in a Coulomb potential (as in a hydrogen atom), the kinetic energy (K.E.) is equal to the negative of the total energy:

K.E. = −E Substituting the total energy we calculated: K.E. = −(−3.4) = 3.4 eV

Now, we need to find the value of x in the form of x × 10^-1 eV. 3.4 eV = 34 × 10^-1 eV Therefore, the value of x is 34. Final Answer x = 34