Physics: In the bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is approximately 0.522 ✕ 10-10 m. (the actual value is 0.529 ✕ 10-10 m.) (a) find the magnitude of the electric force exerted on each particle. (b) if this force causes the centripetal acceleration of the electron, what is the speed of the electron?

In the bohr theory of the hydrogen atom, an electron

nathanbrockdac

02.01.2022

a) $8.5\times 10^{-8}$ N

b) $2.2\times 10^{6}$ m/s

Explanation:

= radius of the orbit = 0.522 x 10⁻¹⁰ m

= magnitude of charge on each proton and electron = 1.6 x 10⁻¹⁹ C

Using coulomb's law , magnitude of electric force on the particle is given as

$F = \frac{k q^{2} }{r^{2} }$

$F = \frac{(9\times 10^{9})(1.6\times 10^{-19})^{2}}{(0.522\times 10^{-10})^{2}}$

$F = 8.5\times 10^{-8}$ N

= mass of electron = 9.1 x 10⁻³¹ kg

= speed of electron = ?

Centripetal force is being provided by the electric force, hence

Centripetal force = electric force

$\frac{mv^{2}}{r} = F$

$\frac{(9.1\times 10^{-31})v^{2}}{0.522\times 10^{-10}} = 8.5\times 10^{-8}$

$v = 2.2\times 10^{6}$ m/s

0,0(0 оценок)