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 wavelenght of the light emitted when the electron returns to the ground state? The ground state electron energy is `-2.18 xx 10^(-11)` ergs.

Explanation

`E_(n)=-(2.178 xx 10^(-18))/(n^2) " J atom"^(-1)`
`triangleE=E_(5)-E_(1)`
`=2.178 xx 10^(-18) (1/1^2-1/5^2)`
`=2.091 xx 10^(-18) " J atom"^(-1)`
The same energy is relased in the returning of the excited electron to the ground state.
`triangleE=hv=h c/lambda`
`lambda=(hc)/(triangleE)=(6.626 xx 10^(-34) xx 3 xx 10^(8))/(2.091 xx 10^(-18))`
`=9.51 xx 10^(-8)m=951A`