Question

Order of number of revolution/sec ${\gamma }_1,{\gamma }_2,{\gamma }_3$ and ${\gamma }_4$ for I, II, III and IV orbits is:

• A. ${\gamma }_1>{\gamma }_2>{\gamma }_3>{\gamma }_4$
• B. ${\gamma }_4>{\gamma }_3>{\gamma }_2>{\gamma }_1$
• C. ${\gamma }_1>{\gamma }_2>{\gamma }_4>{\gamma }_3$
• D. ${\gamma }_2>{\gamma }_3>{\gamma }_4>{\gamma }_1$

Answer 1

The correct option is A ${\gamma }_1>{\gamma }_2>{\gamma }_3>{\gamma }_4$

Order of number of revolution/sec ${\gamma }_1,{\gamma }_2,{\gamma }_3,{\gamma }_4$ for I, II, III and IV orbits is
${\gamma }_1>{\gamma }_2>{\gamma }_3>{\gamma }_4$
The number of revolution/sec $=-\frac{E_1}{h}\left[\frac{2}{n^3}\right]$
For orbit I, the number of revolution/sec $=-\frac{E_1}{h}\left[\frac{2}{1^3}\right]=-\frac{E_1}{h}\times 2$
For orbit II, the number of revolution/sec $=-\frac{E_1}{h}\left[\frac{2}{2^3}\right]=-\frac{E_1}{h}\times 0.25$
For orbit III, the number of revolution/sec $=-\frac{E_1}{h}\left[\frac{2}{3^3}\right]=-\frac{E_1}{h}\times 0.074$
For orbit IV, the number of revolution/sec $=-\frac{E_1}{h}\left[\frac{2}{4^3}\right]=-\frac{E_1}{h}\times 0.03125$