Question

Calculate the energy of electron transitions in a one-electron (bohr) system

Question

What is the wavelength of a photon that will excite an electron from n=3 to n=5 in a hydrogen atom?

• Use R∞=2.179×10−18J for the hydrogen atom Rydberg constant.
• Use h=6.626×10−34 Js for Planck's constant.
• Use c=2.998×108ms for the speed of light.

Answer 1

the energy of electron transitions in a one-electron (bohr) system :

wavelength of a photon that will excite an electron from n=3 to n=5 in a hydrogen atom?

We have :

• R∞=2.179×10⁻¹⁸J ( hydrogen atom Rydberg constant.}
• h=6.626×10⁻³⁴ Js ( Planck's constant.)
• c=2.998×10⁸ ms ( speed of light

from one-electron bohr model dE =  (hc/ ) = R∞ ((1/n₁²) -(1/n₂²)

• we have, n₁= 3 (obital from where electron under going excitation by absorption of  light : lower in energy (more negative energy)) ;  

  n₂=5 (obital where excited electron will reach : higher in energy (less negative energy).

dE =  (hc/ ) =2.179×10⁻¹⁸J  ((1/3²) -(1 / 5²))

dE =  (hc/ ) = 1.5495×10⁻¹⁹J

(6.626×10⁻³⁴ Js* 2.998×10⁸ ms/ ) = 1.5495×10⁻¹⁹J

= 1.282*10⁻⁶ m

(1 nm = 10^-9 m )

= 1282 nm