Question

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

Answer 1

Answer:

(a) Electric force will be $77.285\times 10^{-9}N$

(B) Velocity $v=2.1522\times 10^6m/sec$

Explanation:

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

Charge on electron $e=1.6\times 10^{-19}C$

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

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

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

We know that centripetal force is given by $F=\frac{mv^2}{r}$

So $\frac{9.11\times 10^{-31}\times v^2}{0.546\times 10^{-10}}=77.285\times 10^{-9}$

$v=2.1522\times 10^6m/sec$