Question

An electron in an atom revolves around the nucleus in an orbit of radius 0.53 Å. If the frequency of revolution of an electron is 9 × 10⁹ MHz, calcu-late the orbital angular momentum. [Charge on an electron = 1.6 × 10^-19 C, gyromagnetic ratio = 8.8 × 10¹⁰ C/kg, π = 3.142]

Answer 1

Data : r = 0.53 Å = 0.53 × 10^-10 m,

f = 9 × 10⁹ MHz = 9 × 10¹⁵ Hz, e = 1.6 × 10^-19

C, gyromagnetic ratio = 8.8 × 10¹⁰ C / kg, π = 3.142

Magnetic moment, M₀ = IA = efπr²

= 1.6 × 10^-19 × 9 × 10¹⁵ × 3.142 × (0.53 × 10¹⁰)²

= 14.4 × 3.142 × (0.53)² × 10^-19 × 10¹⁵ × 10²⁰

= 1.272 × 10^-23 A∙m²

Gyromagnetic ratio = \(\cfrac{M_0}{L_0}\)

\(\therefore\) Orbital angular momentum, L₀