Question

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

Answer 1

Explanation:

Two elliptical orbits are added by Sommerfeld in third Bohr’s orbit. In an attempt to account for the structure (splitting) of line spectra known as fine spectra, Sommerfeld added these elliptical orbits.

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Answer 2

Three elliptical orbits Sommerfeld had added to Bohr's fourth orbit.

Explanation:

For the fourth Bohr's orbit , n = 4

here n = principal quantum number, k = azimuthal quantum number,

b = Length of semi minor axis , a = Length of semi major axis

For n = 4, the possible values of k are 1,2,3,4

now, when n = 4, k = 4

$\frac{a}{b}=\frac{k}{n}=\frac{4}{4}=1$    [ since $\frac{a}{b}= 1$ it is Circular orbit]

when n=4 , k= 3

$\frac{a}{b} =\frac{k}{n} =\frac{3}{4}$   [ since $\frac{a}{b}$ < 1 it is elliptical orbit]

when n = 4, k = 2

$\frac{a}{b} =\frac{k}{n} =\frac{2}{4}$    [ since $\frac{a}{b}$ < 1 it is elliptical orbit ]

when n = 4, k = 1

$\frac{a}{b} =\frac{k}{n} =\frac{1}{4}$  [ since $\frac{a}{b}$ < 1 it is elliptical orbit ]

so 3  elliptical orbits Sommerfeld had added to Bohr's

fourth orbit.