Question

where lo, l1 are the angular momentum quantum numbers for the lower and upper states respectively of the atomic transition (s,p, d,...or 1-0, 1, 2, . . .). For example, for the 4s-3p transition for sodium (see Fig. 1 below) has n0-3, nı = 4, 10-1, 11-0 Transition levels of Sodium 6s 4.0 d series s series 2. Ep-3 p series Figure T: Transition levels for the neutral sodium atom The 3p-3s transition produces strong yellow emission spectral lines called the sodium doublet Table 1 provides the quantum defects for various values of n and I. For example, A(n 6,1-3)0.008 Table 1: Dependence of the quantum defect on quantum numbers n and l Termn 3 4 8 l-0 1.373 1.357 1.352 1.349 1.348 1.351 p 0.883 0.867 0.862 0.859 0.858 0.857 l-2d0.01 0.011 0.013 0.011 0.009 0.013 0.000 0.0010.008 -0.012 -0.015 a) Using this equation, write down the Rydberg-like equations for the s series, pseries and d series transitions Hint: These will be three equations of the form of the equation above, with no, lo and l1 replaced with their values. The quantum number n1 will remain in the equation, but you will state which values ni can take A(n,l) known as the quantum defect. Write down the equation used to convert wavelength to energy? Does this equation give energy in Joules or electron volts? How do you convert between Joules and electron volts? b) c) Take the limit of the equation provided in a) as n -oo. Use this to find an expression for oo-3p, and hence Fo-3p 00-3

Answer 1

&s series- lowest value of n can be 3 so n^ = 3, for s seires-,-L and O 3-0.003 Table 1: Dependerce of the quantum defect on quantum numbers n 31.357 1.352 1.349 1.348 1.351 867 .B52 0.5 085B 0B57 1-2 d |001|0011 0.013 | 0.011 | 0.009 0.013 -3 f0000.001-0008 0012 0015 for p series- from picture- - 1.373 R0 377) - - for d-series- from picture above 3-b-Спза - R (0 223 n,-A(n,2) energy E this equation gives energy in joules. we can convert between joules and electron volts using following formula. Il use eq.1 foroto 3p transition- we'l 4464