Question

An electron(e) is revolving in a circular orbit of radius r in the hydrogen atom. The angular momentum of the electron is (M = magnetic dipole moment associated with it and m = mass of electron)

विकल्प

• `"mM"/"e"`

• `"3mM"/"e"`

• `"2mM"/"e"`

• `"4mM"/"e"`

Answer 1

`"2mM"/"e"`

Explanation:

The angular momentum of electron is given as L = mvr = m(rω) · r = mωr²

⇒ `omega"r"^2="L"/"m"`    ...(i)

Magnetic dipole moment,

`"M"="iA"="e"/"T"*pi"r"^2="e"/(2pi//omega)*pi"r"^2="e"/2*omega"r"^2`

⇒ `"M"="e"/2*"L"/"m"`   [From Eq. (i)]

⇒ `"L"=(2"mM")/"e"`