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

Calculation of energy required
The energy of electron `(E_(n))=(-2.18 xx 10^(-11))/(n^(2))"ergs" =(-2.18 xx 10^(-18)J)/(n^(2)) " " (.:' 1J=10^(7)"ergs")`
The energy in Bohr's first orbit `(E_(1))=(-2.18xx10^(-18)J)/((1)^(2))=(-2.18xx10^(-18)J)/(1)`
The energy in Bohr's fifth orbit `(E_(5))=(-2.18xx10^(-18)J)/((5)^(2))=(-2.18xx10^(-18)J)/(25)`
`:." "` Energy required `(DeltaE)=E_(5)-E_(1)=((-2.18)/(25)xx10^(-18)J)-(-(2.18)/(1)xx10^(-18)J)`
`=2.18 xx 10^(-18)(1-(1)/(25))J`
`=2.18 xx 10^(-18)xx24//25=2.09xx10^(-18)J`
Step II. Calculation of wavelength of light emitted
`DeltaE=hv=(hc)/(lambda)`
`:. " " lambda =(hc)/(DeltaE)=((6.626xx10^(-34)J-s)xx(3xx10^(8) ms^(-1)))/((2.09xx10^(-18)J))`
`=9.50xx10^(-8)m=950Ã…. " " (.:'1 Ã…=10^(-10)m)`