Question

A hydrogen atom initially in the ground level absorbs a photon,which excites it to the n = 4 level. Determine the wavelength andfrequency of photon.

Answer 1

This is given that hydrogen atom initially at ground level absorbs photon and excites it to the n=4level.

Energy related to photon is given as,

E n = −13.6 n 2  eV

For ground level n=1,

E 1 = −13.6 1 2 =−13.6 eV

Let E 2 be the energy when atom is excited at higher level n 2 =4,

E 2 = −13.6 4 2  eV =− 13.6 16  eV

Energy absorbed by the photon is given as,

E= E 2 − E 1 =− 13.6 16 −( −13.6 1 ) = 13.6×15 16 ×1.6× 10 −19 =2.04× 10 −18  J

Energy of photon of wavelength λis given as follows,

E= hc λ

where, Planck’s constant, h=6.6× 10 −34  Js, Speed of light, c=3× 10 8  m/s

Substitute the value of E, h and cin the above equation.

λ= 6.6× 10 −34 ×3× 10 8 2.04× 10 −18 =9.7× 10 −8  m

Frequency of photon is given as,

ν= c λ = 3× 10 8 9.7× 10 −8 =3.1× 10 15  Hz

Thus, the wavelength of photon is 9.7× 10 −8  mand the frequency is 3.1× 10 15  Hz.