Question

. An electron in an atom is revolving round the nucleus in a circular orbit of radius 5.3 * 10-11 m. with a speed of 4 x 10^6ms. Find the resultant orbital magnetic moment and angular momentum of electron.​

Answer 1

Answer:

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Answer 2

Answer:

The resultant orbital magnetic moment and angular momentum of the electron are 1.696×10⁻²³Am² and 1.9292 ×10⁻³⁴kgm²/s respectively.

Explanation:

The orbital magnetic moment of an electron is given as,

$M=\frac{evr}{2}$       (1)

And the angular momentum of an electron is given as,

$L=mvr$      (2)

From the question we have,

The radius of the electron(r)=5.3×10⁻¹¹m,

Speed of the electron (v)=4× 10⁶m/s

Mass of an electron=9.1×10⁻³¹kg

Charge on an electron(e)=1.6× 10⁻¹⁹C

By substituting the required values in equation (1) we get;

$M=\frac{1.6\times 10^-^1^9\times 4\times 10^6\times 5.3\times 10^-^1^1}{2}=16.96\times 10^-^2^4=1.696\times 10^-^2^3Am^2$

By substituting the required values in equation (2) we get;

$L=9.1\times 10^-^3^1\times 4\times 10^6\times 5.3\times 10^-^1^1=192.92\times 10^-^3^6=1.9292\times 10^-^3^4 kgm^2/s$

Hence, the resultant orbital magnetic moment and angular momentum of the electron are 1.696×10⁻²³Am² and 1.9292 ×10⁻³⁴kgm²/s respectively.