What is the energy in joules, requried to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Borh orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is `-2.18xx10^(-11)` erg.

Explanation

Given: Energy of ground state `(E_(1))=-2.18xx10^(-11)` erg
`therefore`Energy of n-th orbit, `E_(n)=(E_(1))/(n^(2))erg=(-2.18xx10^(-11))/(n^(2))`erg
The amount of energy required when an electron jumps from 1st-orbit to 5th-orbit,
`DeltaE=E_(5)-E_(1)=(-2.18xx10^(-11))/(5^(2))-(-2.18xx10^(-11))`
`=2.18xx10^(-11)(1-(1)/(25))`
`=2.092xx10^(-11)erg=2.092xx10^(-18)J" "[because1erg=10^(-7)]`
The amount of energy released when the electron returns from 5th-robit to 1st-orbit=`2.092xx10^(-11)erg`
we know that, `DeltaE=hv=h(c)/(lamda)`
or, `(hc)/(DeltaE)=((6.626xx10^(-27)erg*s)xx(3xx10^(10)cm*s^(-1)))/(2.092xx10^(-11)erg)`
`=9.501xx10^(-6)cm=950xx10^(-8)cm=950` Å