Answer:
a) [tex]8.5\times 10^{-8}[/tex] N
b) [tex] 2.2\times 10^{6}[/tex] m/s
Explanation:
a)
[tex]r[/tex] = radius of the orbit = 0.522 x 10⁻¹⁰ m
[tex]q[/tex] = 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
[tex]F = \frac{k q^{2} }{r^{2} }[/tex]
[tex]F = \frac{(9\times 10^{9})(1.6\times 10^{-19})^{2}}{(0.522\times 10^{-10})^{2}}[/tex]
[tex]F = 8.5\times 10^{-8}[/tex] N
b)
[tex]m[/tex] = mass of electron = 9.1 x 10⁻³¹ kg
[tex]v[/tex] = speed of electron = ?
Centripetal force is being provided by the electric force, hence
Centripetal force = electric force
[tex]\frac{mv^{2}}{r} = F[/tex]
[tex]\frac{(9.1\times 10^{-31})v^{2}}{0.522\times 10^{-10}} = 8.5\times 10^{-8}[/tex]
[tex]v = 2.2\times 10^{6}[/tex] m/s
