Question

ahydrogen atom initially in the ground state absorbs a photon which excites into the n=4level estimate the frequency of the photon

Answer 1

Energy of the ground level

E1= -13.6/ n12 = -13.6/1 = -13.6 eV

For higher level (n2)=4

Energy of the ground level

E2= -13.6/ n22 = -13.6/(4)2 = -13.6/16 = -0.85 eV

The energy absorbed by a photon,

E = E1 - E2

   = -0.85 - (-13.6)

    = -0.85 +13.6

   = 12.75 eV

   = 12.75 x 1.6 x 10-19

  = 20.4 x 10-19

  = 2.04 x 10-18 J

For, a photon of a wavelength

E=hc/λ       Where, h= 6.6 x x 10-34  J, C = speed of light = 3 x x 108 m/s

Therefore,

E=hc/λ      

λ = hc/E

  = 6.6 x x 10-34 x 3 x 108/2.04 x 10-18

  = 9.7 x 10-8 m

  = 97 nm

Frequency

v=c/λ  

  = 3 x 108/9.7 x 10-8

 = 3.1 x 1015 Hz

Hence, wavelength of photon is 97 nm and frequency is 3.1 x 1015 Hz