The lifetime of hydrogen in the 2p state to decay to the is

The lifetime of hydrogen in the 2p state to decay to the is ground state is 1.6 Times 10^-9. The lifetime transmission is therefore Estimate the uncertainty deltaE in energy of this excited state. What is the corresponding linewidth in angstroms?

Solution

Using uncertainty principle of energy time

E.t = h/4, h is Planks constant

Life time of the state is the uncertainty t = 1.6e-9 s

Uncertainty E = 6.58x10^-16/2x1.6x10^-9 (h/2 = 6.58e-16 ev-s)

                             =2.056e-7 ev

E= hf = h/,   (f is line width in Hz and line width in wavelength in m)

Uncertainty in wavelength or the line width

        = h/E = 4.136x10^-15/2.056x10^-7

                =    2.011 x10^-8 m

                 = 201.1 A⁰   (1 A⁰ = 10^-10 m)