Question

Data Report Sheet: The Atomic Spectra of Hydrogen A. Table 1: The Energy Levels of the Hydrogen Atom Quantum Number, n Energy, kJ/mol Quantum Number, Energy, E, k/mol 1 -2.18x10/1--2.18x10J 2 -2.18x10"/2--5.45x10 B. Table 2. Calculation of Wavelengths Associated with Energy Transitions 2 1 3 4 5 E, -E, AE- 1.64 x 10J AE k.J/mol , nm thc/AE)- 121.5nm AE kJ/mol nm AE kJ/mol 3 , nm AE kJ/mol nm AE kJ/mol 5 7, nm 55 Table 3: Assignment of Observed Lines in the Hydrogen Spectrum C Assignment Wavelength, Wavelength, Assignment Wavelength, nm Assignment nm 410.29 1005.2 97.26 434.17 1094.1 102.57 486.27 121.57 1282.2 656.47 389.02 1875.6 954.86 397.12 40452.3 The lines of the Balmer series lie between 250 nm and 700 nm. Based upon your assignments, what do all of the lines of the Balmer series have in common? What is the transition associated with the longest wavelength possible in the Balmer series? What is the transition associated with the shortest wavelength possible in the Balmer series?

Answer 1

All lines of balmer series have n1= 2.....the n2 can take any positive baluee

According to Balmer formula

ṽ=1/λ = R_H[1/n₁²-1/n₂²]

For the Balmer series, n_i = 2.

Thus, the expression of wavenumber(ṽ) is given by,

Wave number (ṽ) is inversely proportional to wavelength of transition. Hence, for the longest wavelength transition, ṽ has to be the smallest.

For ṽ to be minimum, n_f should be minimum. For the Balmer series, a transition from n_i = 2 to n_f = 3 is allowed. Hence, taking n_f = 3,we get:

ṽ= 1.5236 × 10⁶ m^–1.

^{similarly above calculations...the transitions associated with shortest wavelength is n1 =2 and n3= infinity.}