Photon's Energy: Chemistry

Question

Calculate the energy (in J) of a photon emitted during a transition corresponding to the third line in the Lyman series (n_f = 1) of the hydrogen emission spectrum.

(Report your answer to three significant figures.)

Answer 1

There may be an easier/quicker/simpler way to do this, but this is the way I understand it best. So, here goes.

 

The first line is generated when an electron falls from n=2; second line is when an electron falls from n=3 and the third line is when an electron falls from n=4.  Thus, for this problem n_i = 4 and n_f = 1

 

We can use the equation 1/λ = R(1/n_f² - 1/n_i²) where R is the Rydberg constant = 1.097x10⁷ m^-1

1/λ = 1.097x10⁷ m^-1 (1- 1/16) = (1.097x10⁷ m^-1)(0.9375) = 1.028x10⁷m^-1

λ = 1/1.028x10⁷ m^-1 = 1.00x10^-7 m 

 

E = hc/λ where h is Planck's constant = 6.626x10^-34 Jsec and c = speed of light = 3x10⁸ msec^-1

E = (6.626x10^-34)(3x10⁸)/1.00x10^-7 = 1.99x10^-19 J

 

Caveat:  It's a good/great idea to check my math.  But I believe the process/method is a correct one.

 

Answer 2

This answer was deleted by Arturo O.