An atom in its ground state absorbs a single photon of light and then relaxes back to the ground state by emitting an infrared photon (1,200 nm) followed by an orange photon (600 nm). Calculate the energy and frequency of the photon that was absorbed initially.

Frequency  OF absorbed photon =7.497 x 10^14 s^-1 ,Energy OF absorbed photon =4.97 X 10 ^-19J

Explanation:

The formula for ansorbd wavelength is given as

1/λabs = 1/λ1 + 1/λ2

1/λabs = 1/1200nm + 1/600nm

1/λabs = 0.0008333 +0.0016666

1/λabs =0.002499

λabs= 1/002499

λabs= 400.16nm

a

But Frequency =f = c / λ

Where

speed c =  3.0 x 10^8 m/s

wavelength λ (m) = 4.0016 x 10^-7m

Frequency = 3.0 x 10^8 m/s/ 4.0016 x 10^-7m = 7.497 x 10^14 s^-1

And energy = hc/ λ

h= Plank constant

c= speed of light

λ= Wavelength=4.0016 x 10^-7m

E= 6.626 X 10-34Js X  3.0 x 10^8 m/s/ 4.0016 x 10^-7m

Energy = 4.9675 x 10 ^-19J = 4.97 X 10 ^-19J