Energy (E) of the nth Bohr orbit of an atom is given by,
`"E"_"n" = (-(2.18xx10^(-18))"Z"^2)/"n"^2`
Where,
Z = atomic number of the atom
Ground state energy = – 2.18 × 10–11 ergs
= - 2.18 × 10–11 × 10–7 J
= - 2.18 × 10–18 J
Energy required to shift the electron from n = 1 to n = 5 is given as:
ΔE = E5 – E1
`= (-(2.18xx10^(-18))(1)^2)/(5)^2 - (-2.18 xx 10^(-18))`
`= (2.18xx10^(-18))[1 - 1/25]`
`= (2.18xx10^(-18))(24/25)`
`= 2.0928 xx 10^(-18)"J"`
Wavelength of emitted light = `"hc"/"E"`
`= ((6.626xx10^(-34))(3xx10^(8)))/(2.0928xx10^(-18))`
`= 9.498 xx 10^(-8) "m"`
Text Solution
Solution : Energy (E) of the nth Bohr orbit of an atom is given by, <br> `E_(0) = (-(2.18xx 10^(-18))Z^(2))/(n^(2))` <br> where , <br> Z = atomic number of the atom <br> Ground state energy `=-2.18xx10^(-11) ergs` <br> `=- 2.18xx 10^(-11)xx 10^(-7) J` <br> `-2.18 xx 10^(-18) J ` <br> Energy required to shift the election from n=1 to n= 5 is given as . <br> `deltaE =E_(5) - E_(1)` <br> `=((2.18 xx 10^(-18)) (1)^(2))/((5)^(2))-(-2.18xx 10^(-18))` <br> `(2.18xx10^(-18) ) [1-1/25]` <br> ` (2.18xx 10 ^(-18) ) (24/25) = 2.0928xx 10^(-18)) J ` <br> wavelength of emitted light = `(hc)/E` <br> `((6.626xx 10^(-34))( 3xx 10^(8)))/((2.0928 xx 10^(-18))` <br> `= 9.498xx 10^(-8) m `