Answer to Question #185069 in Mechanics | Relativity for Jay

Question

In Bohr’s model of the hydrogen atom, the electron travels with speed 2.2 x 10⁶m/s in a circle (r= 5.3 x 10^-11m) about the nucleus. Find the value of B at the nucleus due to the electrons motion. Assume vacuum.

Answer 1

To be given in question

Speed of electron (V)=$2.2\times10^6 meter/sec$

Radius of circle (r)=$5.3\times10^{-11}meter$

Mass of electron$(m)$ =$9.1\times10^{-31} kg$

Charge of electron$(q)$ =$1.6\times20^{-19}C$

To be asked in question

Magnetic field (B)=?

We know that

Magnetic force=centripetal force

$qvB =\frac{mv^2}{r} \rightarrow(1)$

$B=\frac{mv}{qr}\rightarrow(2)$

Put value in eqution (2)

$B=\frac{9.1\times10^{-31}\times2.2\times10^6}{1.6\times10^{-19}\times5.3\times10^{-11}}$

$B=236084.9057 tesla$

$B=2.36084\times10^5 T$