In Sommerfeld's modification of Bohr's theory, the trajectory of an electron in a hydrogen atom is
A.Perfect ellipse
B.a closed ellipse like curve, narrower at the perihelion position and flatter at the aphelion positron
C.a closed loop on spherical surface
D.a rosette

Hint: To answer this question, you should recall the concept of Sommerfeld theory of atomic structures. It explains the spectrum of the hydrogen atom and also the shape of the orbit of an atom.

Complete step by step answer:
We know the postulates of Sommerfeld theory:
-Explains the fine spectrum of Hydrogen atoms.
-It states that the orbit of atoms may be both circular or elliptical.
-In case the orbit is elliptical, then there are two axis – major axis & minor axis. When the length of major & minor axis becomes equal then orbit is circular.
-According to Bohr's theory, you should know that the electrons in an atom after receiving incident energy move from a lower energy level to a higher energy level. This phenomenon occurs by the gain of energy where an electron moves from a higher energy level to lower energy level by losing energy. This energy is lost in the form of spectral lines. Hence spectral series can be defined as a set of wavelengths arranged sequentially with the characteristic feature of every atom. The emitted wavelengths are resolved using a spectroscope.
-Also, this model states that negatively charged particles called electrons revolve around the positively charged nucleus in a definite circular path called orbits or shells. These shells have a fixed energy state which is different for every shell. The shells are designated with integers . This value is called the principal quantum number.

Hence,the correct option is option D, i.e. a rosette.

Note:
Scientists have now developed the new and more generalized Bohr–Sommerfeld theory described the atom in terms of two quantum numbers. This is better than the previous Bohr model theory which used only one quantum number.