The value of ground state energy of hydrogen atom is - 13.6 eV.
(a) Find the energy required to move an electron from the ground state to the first excited state of the atom.
(b) Determine (i) the kinetic energy, and (ii) the orbital radius in the first excited state of the atom.
(Given the value of Bohr radius ` = 0.53Å`)

Explanation

(a) `because` Ground state energy of electron (n = 1) is E = - 13.6 eV
`therefore ` Energy for first excited state `(n =2) E_(2) =(-13.6)/(n^(2)) = (-13.6)/((2)^(2)) = - 3.4 eV`
`therefore ` Energy required to be given to electron `Delta E = E_(2) - E_(1) = - 3.4 - (-13.6) = + 10.2 eV`
(b) (i) Kinetic energy of electron in 1st excited state `K_(2) = -E_(2) = + 3.4 eV`
(ii) Orbital radius in first excited state `r_(2) = n^(2) a_(0) = (2)^(@) xx 0.53 Å = 2.12 Å`