What is the energy in joules required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr 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 18 xx 10 ^(-11)` erg.

Explanation

Energy (E) of the nth Bohr orbit of an atom is given by,
`E_(0) = (-(2.18xx 10^(-18))Z^(2))/(n^(2))`
where ,
Z = atomic number of the atom
Ground state energy `=-2.18xx10^(-11) ergs`
`=- 2.18xx 10^(-11)xx 10^(-7) J`
`-2.18 xx 10^(-18) J `
Energy required to shift the election from n=1 to n= 5 is given as .
`deltaE =E_(5) - E_(1)`
`=((2.18 xx 10^(-18)) (1)^(2))/((5)^(2))-(-2.18xx 10^(-18))`
`(2.18xx10^(-18) ) [1-1/25]`
` (2.18xx 10 ^(-18) ) (24/25) = 2.0928xx 10^(-18)) J `
wavelength of emitted light = `(hc)/E`
`((6.626xx 10^(-34))( 3xx 10^(8)))/((2.0928 xx 10^(-18))`
`= 9.498xx 10^(-8) m `