Calculate the energy required to excite hydrogen atom from ground state to the second excited state

Explanation

Data supplied
` m=9 xx 10^(-31) Kg , c = 3 xx 10^8 m//s , alpha =(1)/( 137 )`
For ground state `n_f = 3`
energy required ` =E_(3!) = E_3 - E_1 = (mc ^2 alpha ^2)/(2) [ (1)/(I^2 ) - (1)/( 3 ^2) ] = (mc^2 alpha^2 )/(2)((8)/(9))`
` therefore E_(31) = ( 9xx 10^(-31) xx(2 xx 10 ^8 )^2 xx 8) /( 2xx 137 xx 137 xx 9)` joules
` E_(31) =( 9xx 9xx 8 xx 10^(-31) xx 10^(16) )/( 2xx9xx 137 xx 137 xx 1.6 xx 10 ^(-19)) eV = 11.98 eV ` [ since `, 1 eV = 1.6xx 10^(-19)J`]