Question

A ground state hydrogen atom absorbs a photon of λ = 94.91 nm, exciting the electron to a higher energy (quantum) level. The electron then decays to a lower, intermediate energy level, emitting a photon of λ = 1281 nm. From that intermediate energy level the electron decays back to the ground state, emitting another photon. a) What is the highest energy level attained by the electron?

b) What was the intermediate energy level of the electron?

c) What was the λ of the second photon?

Answer 1

Wavelength (l)   (absorbed ) photon absorbed by H at ground state = 94.91 nm

Wavelength emitting photon to intermediate level l (emission )= 1281 nm

a). highest energy level attained by electron.

We can calculate energy absorbed by photon by using absorbed wavelength.

Equation:

E = hc/l   , E is energy in J , h = planks constant( 6.626E-34 Js) , C is speed of light = 3.0 E 8 m/s , l is wavelength in m

Lets plug given values in above equation.

E = [( 6.626 E-34 Js x 3.0 E8 m/s)/ (94.91 E-9 m ) ]   

(we used 1 nm = 10^-9 m relation)

E = 2.094 E-18 J

This is highest energy that that can be absorbed by electron while going in excited state from ground state.

b) Intermediate energy level of electron.

Here we use wavelength of emitted electron to find out intermediate energy level.

In this we first calculate energy of emitted electron and then by subtracting it from highest energy we get intermediate energy level.

We use same equation:

E = [( 6.626 E-34 Js x 3.0 E8 m/s)/ (1281 E-9 m ) ]   

=1.552 E-19 J

Energy of intermediate = E (highest) – E (lowest)

= 2.094 E-18 J – 1.552 E-19 J =1.94 E-18 J

So the intermediate energy level at = 1.94 E-18 J

c ) Calculation of wavelength of second photon.

This has exactly the energy of intermediate level since it falls from it to ground level.

Lets rearrange same equation to get wavelength.

l = hc / E

l = [( 6.626 E-34 Js x 3.0 E8 m/s)/ (1.94 E-18 ) ]   

=1.025 E-7 M

Wavelength in nm = 1.025 E-7 x 1 nm / 1E-9 m

= 102.5 nm