Answer:
Radius between electron and proton[tex] = 6.804\times 10^{-10}m[/tex]
Explanation:
The motion of the electron is carried out in the orbit due to the balancing of the electrostatic force between the proton and the electron and the centripetal force acting on the electron.
The electrostatic force is given as = [tex]\frac{kq_1q_2}{r^2}[/tex]
Where,
k = coulomb's law constant (9×10⁹ N-m²/C²)
q₁ and q₂ = charges = 1.6 × 10⁻¹⁹ C
r = radius between the proton and the electron
Also,
Centripetal force on the moving electron is given as:
=[tex]\frac{m_eV^2}{r}[/tex]
where,
[tex]m_e[/tex] = mass of the electron (9.1 ×10⁻³¹ kg)
V = velocity of the moving electron (given: 6.1 ×10⁵ m/s)
Now equating both the formulas, we have
[tex]\frac{kq_1q_2}{r^2}[/tex] = [tex]\frac{m_eV^2}{r}[/tex]
⇒[tex]r = \frac{kq_1q_2}{m_eV^2}[/tex]
substituting the values in the above equation we get,
[tex]r = \frac{9\times 10^{9}\times (1.6\times 10^{-19})^2}{9.1\times 10^{-31}\times (6.1\times 10^5)^2}[/tex]
⇒[tex]r = 6.804\times 10^{-10}m[/tex]
