What is the energy in joules required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth for B?

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 `