Coulombs' law for electrostatic force between two point charges and Newton's law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges/masses.
(a) Compare the strength of these forces by determining the ratio of their magnitude
(i) for an electron and a proton and (ii) for two protons.
(b) Estimate the accelerations for electron and proton due to the electrical force of their mutual attraction when they are 1Å (= 10−10 m) apart? mp = 1.67 ✕ 10−27 kg m e = 9.11 ✕ 10−31 kg.
Answers
We know
charge of an electron = -1.67 ×10⁻¹⁹ C
charge of an proton = 1.67 ×10⁻¹⁹ C
Mass of electron = 9.1 × 10⁻³¹ kg
Mass of proton = 1.67 × 10⁻²⁷ kg
(a). (i)
(Coulomb force/Gravitational force)
= {(9 ×10⁹×(-1.6×10⁻¹⁹)1.6×10⁻¹⁹)/r²}/{(6.67×10⁻¹¹×9.1×10⁻³¹×1.67×10⁻²⁷)/r²}
= 23.04×10⁻²⁹/101.36×10⁻⁶⁹
= 0.2273×10⁻⁴⁰
=2.27×10⁻³⁹
(ii)(Coulomb force/Gravitational force)
= {(9×10⁹×(1.6×10⁻²⁹)²/r²)}/{6.67×10⁻¹¹×(1.67×10⁻²⁷)²/r²}
=1.24×10³⁶
(b)
Force F = 9×10⁹(-1.6×10⁻¹⁹)×1.6×10⁻¹⁹/(10⁻¹⁰)²
F = 2.304 × 10⁻⁸ N
And we know Force F = mass × acceleration
Hence acceleration of electron = F/m = 2.304 × 10⁻⁸ N/ 9.1 × 10⁻³¹ kg
a₁ = 2.5 × 10²² m/s²
and acceleration of proton a₂ = 2.304 × 10⁻⁸ N/1.67 × 10⁻²⁷ kg
a₂ = 1.4 × 10¹⁹ m/s²
Answer:Hope this might help you out.
Explanation:
(a) (1) |Fe| / |Fg| =2.4 *10^39
(2) |Fe| / |Fg| =1.3 * 10^36
(b) ae= e^2/4piEor^2me =2.5*10^22 m/s^2;
ap=e^2/4piEor^2mp=1.4-10^19 m/s^2