Question

9. How many elliptical orbits Sommerfeld had added to Bohr's
fourth orbit? Show with the help of a figure.​

Answer 1

Answer:

sommerfield explained further splitting of lines into several lines by assuming that some of the orbital are elliptical in shape .

shape of ellipse defined by

major axis

---------------. = n/k. .............(1). n is principal qn

minor axis

value of k= 1 to n

if ratio is 1 ellipse is circular in shape

k is called azimuthal quatum number or subsidiary quantum number . nowadays it is replaced by l

where l= k-1

so for n =4 principal quantum number

l= 0,1,2,3 k= 4,3,2,1

so ratio represented in eq 1

take values 1,4/3,4/2,4/1

for ratio 1 shape is circular

and for others it is ellipse

which explained that electron transituon not take place only in principal qn. but also in elliptical orbits or subsidiary qn. which explained splitting of spectral lines .

see atrachment for figure where nucleus present in space formed by circle and ellipse formed by k =1.

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