What must be the velocity of electrons if their associated wavelength is equal to the longest wavelength line in the Lyman series?
Express your answer using four significant figures.
Should I be using the Balmer equation?
#\nu=(3.2881\times10^15s^(-1))(1/2^2-1/n^2)#
Or should I apply the Rydberg one?
#1/\lambda=R_\infty(1/n_1^{2}-1/n_2^{2})#
Express your answer using four significant figures.
Should I be using the Balmer equation?
Or should I apply the Rydberg one?
1 Answer
Explanation:
The longest wavelength in the Lyman series corresponds to the
#n=2 -> n=1#
transition and can be calculated using the Rydberg equation
#1/(lamda) = R_(oo) * (1/n_f^2 - 1/n_i^2)#
with
#R_(oo) ~~ 1.097373 * 10^7"m"^(-1)# #n_f = 1# #n_i = 2#
Rearrange to solve for
#lamda = 1/(R_(oo) * (1 - 1/n_i^2))#
Plug in your values to find
#lamda = 1/(1.097373 * 10^(7)"m"^(-1) * (1 - 1/2^2)) = 1.215 * 10^(-7)"m"#
The wavelength of a moving electron is given by the de Broglie expression:
Rearranging:
Putting in the numbers: