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 0.546 ✕ 10-10 m. (The actual value is 0.529 ✕ 10-10 m.) (a) Find the electric force between the two, based on the approximate (not actual) radius given. 7.739e-8 Correct: Your answer is correct. N (b) If this force causes the centripetal acceleration of the electron, what is the speed of the electron? 8.495e22 Incorrect: Your answer is incorrect. m/s

Respuesta :

Answer:

(a) Electric force will be [tex]77.285\times 10^{-9}N[/tex]

(B) Velocity [tex]v=2.1522\times 10^6m/sec[/tex]

Explanation:

We have given that radius of the circular orbit [tex]r=0.546\times 10^{-10}m[/tex]

Charge on electron [tex]e=1.6\times 10^{-19}C[/tex]

(A) According to coulomb's law electric force between two charges is given by

[tex]F=\frac{kq}{r^2}[/tex]

So electric force [tex]F=\frac{9\times 10^9\times (1.6\times 10^{-19})^2}{(0.546\times 10^{-10})^2}=77.285\times 10^{-9}N[/tex]

We know that centripetal force is given by [tex]F=\frac{mv^2}{r}[/tex]

So [tex]\frac{9.11\times 10^{-31}\times v^2}{0.546\times 10^{-10}}=77.285\times 10^{-9}[/tex]

[tex]v=2.1522\times 10^6m/sec[/tex]