Question #2e787
1 Answer
Explanation:
Your tool of choice here will be the Rydberg equation, which looks like this
#1/(lamda) = R * (1/n_f^2 - 1/n_i^2)#
Here
#lamda# is the wavelength of the photon#R# is the Rydberg constant, equal to#1.097 * 10^(7)# #"m"^(-1)# #n_I# is the initial energy level of the transition#n_f# is the final energy level of the transition
Now, you know that the electron starts on an initial energy level
#n_f = 3#
Moreover, you know that this transition is accompanied by the emission of a photon of wavelength
#lamda = 9.54 * 10^(-7)# #"m"#
Rearrange the Rydberg equation to solve for
#1/(lamda) = R * (n_i^2 - n_f^2)/(n_i^2 * n_f^2)#
This is equivalent to
#n_i^2 * n_f^2 = lamda * R * n_i^2 - lamda * R * n_f^2#
#lamda * R * n_i^2 - n_i^2 * n_f^2 = lamda * R * n_f^2#
#n_i^2 * (lamda * R - n_f^2) = lamda * R * n_f^2#
Finally, you should end up with
#n_i = sqrt( (lamda * R * n_f^2)/(lamda * R - n_f^2))#
Plug in your values to find
#n_i = sqrt( (9.54 * color(blue)(cancel(color(black)(10^(-7))))color(red)(cancel(color(black)("m"))) * 1.097 * color(blue)(cancel(color(black)(10^7)))color(red)(cancel(color(black)("m"^(-1)))) * 3^2)/(9.54 * color(blue)(cancel(color(black)(10^(-7))))color(red)(cancel(color(black)("m"))) * 1.097 * color(blue)(cancel(color(black)(10^7)))color(red)(cancel(color(black)("m"^(-1)))) - 3^2))#
#n_ i = 8.017 ~~ color(darkgreen)(ul(color(black)(8)))#
Therefore, you can say that this electron underwent a