Show that the ratio of the magnitic dipole moment to the angular momentum`(l = mvr)` is a universal constant for hydrogen atom and ions find the value

Answer

A, B, C

Explanation

Magnetic dipole moment `=niA`
`=(e xx mc^2 xx pir_2^2n^2)/(2e.h^3n^3)`
Angular momentum `=mvr = (nh)/(2pi)`
Since the ratio of magnetic dipole moment, and angular momentum is independent of 'Z'.
Hence it is a universal constant.
`Ratio = (e^5 xx m xx pir^2n^2)/(24 in_0h^3n^3) xx (2pi)/(nh)`
`=((1.6 xx 10 ^-19)(9.1 xx 10^-31)(3.14)^2 xx (0.53 xx 10^-10)^2)/(2 xx (8.85 xx 10^-12)^2 xx (6.63 xx 10^-34) xx 1^2)`
`=3.78 xx 10^10 C//kg`.