Question

Light from a laser of wavelength 475 nm is incident upon an atom of hydrogen in the first excited state. (a) What is the highest energy level (value of n) to which the hydrogen atom can be excited by the laser?   (b) What happens if the laser wavelength is 295 nm?

Another way to get the energy levels of the Bohr atom is to assume that the stationary states are those for which the circumference of the orbit is an integral number of de Broglie wavelengths. Show that this condition gives the angular momentum criterion, Eq: mvr =n*h(bar), used in Bohr theory.

Answer 1

energy level of hydrogen atom is given by -Eo/n^2

Eo =13.6 eV=13.6*1.602*10^-19 j =21.79*10^-19 J    n = energy level

Energy of a laser with wavelength , E =hc/

h =6.626*10^*34 Js c=3*10^8 m/s =475 nm=475 *10^-9 m

E=hc/ = (6.626*10^-34)(3*10^8)/(475*10^-9)

   E= 4.18*10^-19 Joules

4.18*10^-19 Joules of energy is required to excite an hydrogen aton in first excited state to n excited state

E1 =-13.6/2^2 eV= -3.4eV =-5.45*10^-19 J

   En -E1 =4.18*10^-19j

   En=( 4.18*10^-19 )+(-5.45*10^-19)

En = -1.27*10^-19 J.

but En =-13.6eV/n^2

-1.27*10^-19 =(-21.79*10^-19)/n^2

   n^2=-21.79*10^-19/-1.27*10^-19

   n^2 =17.16

   n=4.14

N =4

IF =295 nm    Energy of the laser =6.73*10^-19 J En = (6.73 -5.45)*10^-19 J

En = 1.28 *10^-19 J

This is more than the binding energy of the hydrogen atom thie will eject the electron out of the outermost orbit