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

Given ,
` E_(n)=(2.18xx 10^(-18))/(n^(2)) J`
energy required for ionization from n = 2 is given by ,
`DeltaE= E_(oo)- E_(2)`
`[(((-2.18xx10^(-18)))/((oo)^(2))) - (((-2.18xx10^(-18)))/((1)^(2)))]J`
`0.545xx10^(-18) J `
`DeltaE= 5.45 xx 10^(-19) J `
`lambda =(hc)/(DeltaE)`
here, `lambda` is the longest wavelength causing the transition.
`lambda =((6.626xx10^(-34))(3xx10^(8)))/(5.45xx 10^(-19)) = 3.647 xx10^(-7) m`
` 3647xx 10 ^(-10)m `
`3647 A`