Question

In interstellar space near a star there is a region called H II in which highly excited H atoms can be produced in the process e + H = H (highly excited). When a highly excited hydrogen atom makes a transition from n = 109 to n= 108 a photon is emitted. Calculate The wavenumber, in cm and wavelength, in nm, of this radiation. The frequency, in sl, of this radiation. The energy, in Joules, of a single photon of this radiation and the energy, in kJ, of 1 mole of this radiation. (i) (iii)

Answer 1

the equation that is to be used for the question is Rydberg's equation

1/λ=R⋅(1/n²_final−1/n²_initial), where

λ - the wavelength of the emitted photon;
R - Rydberg's constant =1.0974 X 10⁷m⁻¹;
n _final - the final energy level - in your case equal to 108
n _initial - the initial energy level - in your case equal to 109

1) wave number is 1/ λ = 1.0974 X 10^7 (1/108^2 - 1/ 109^2) =17.18 m^-1 = 1718cm^-1

^{wave length is} λ = 1/17.18 m =0.058207m = 5.8X10^8nm

2) frequency = C/λ where C is the speed of the light =3X10^8ms^-1/0.058m =51.5463s^-1

^{3) E= hC/}λ  where h is the planks constant

E= 6.626X 10^(-34) x51.54 = 341.50 X10_{^-34 J}

one mole of photon contains avagadro number of photons there fore the energy of avagadro number of photons is = 341.50 X10_{^-34 J} X 6.022x 10²³

= 2056.537 X 10^-11Jmol^-1

   = 2.056X 10^-11KJmol^-1