What is the energy in joules required to shift the elertcon of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit ? And what is the wavelenght of the light emitted when the electron returns to the ground state ? The ground state electron energy is ` -2 18 xx 10 ^(-11)` erg.

Explanation

The ground state energy is `-2.18 xx 10^(-11)` ergs.,
`:. E_n = =-(2.18 xx 10^(-11))/(n^2) ergs`
`Delta E = E_5 - E_1 = -2.18 xx 10^(-11) (1/(5^5) - 1/(1^2))`
`=2.18 xx 10^(-11) xx 24/25 = 2.093 xx 10^(-11) ergs`
or `" " = 2.093 xx 10^(18) J (1 erg = 10^(-7)J)`
when electron returns to ground state (i.e., n = 1), energy emitted = `2.093 xx 10^(-18) J`
Now, `Delta = (hc)/(lambda) " or " lambda = (hc)/(Delta E)`
`= ((6.626 xx 10^(-34) Js) xx (3.0 xx 10^8 ms^(-1)))/((2.093 xx 10^(-18) J))`
`= 9.50 xx 10^(-8) m`
or `" " = 950 Å`.