Question 504: Atoms & Nuclei

Question

The ratio of Coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is 2.4 $$	imes$$ 10
39
. The ratio of the proportionality constant, $$K = {1 \over {4\pi {\varepsilon _0}}}$$ to the gravitational constant G is nearly (Given that the charge of the proton and electron each = 1.6 $$	imes$$ 10
$$-$$19
C, the mass of the electron = 9.11 $$	imes$$ 10
$$-$$31
kg, the mass of the proton = 1.67 $$	imes$$ 10
$$-$$27
kg) :

Accepted Answer

Ratio of magnitude of Coulomb's electrostatic force to the gravitational force
$${{{F_E}} \over {{F_G}}} = {{\left( {{{K{q_1}{q_2}} \over {{r^2}}}} ight)} \over {\left( {{{G{m_1}{m_2}} \over {{r^2}}}} ight)}} = {{K{q_1}{q_2}} \over {G{m_1}{m_2}}}$$
$$ \Rightarrow 2.4 	imes {10^{39}} = {K \over G} 	imes {{1.6 	imes {{10}^{ - 19}} 	imes 1.6 	imes {{10}^{ - 19}}} \over {9.11 	imes {{10}^{ - 31}} 	imes 1.67 	imes {{10}^{ - 27}}}}$$
$$ \Rightarrow 2.4 	imes {10^{39}} = {K \over G} 	imes {{2.56} \over {15.21}} 	imes {10^{20}} \Rightarrow {K \over G} = 14.26 	imes {10^{19}}$$
$$ \Rightarrow {K \over G} = 1.426 	imes {10^{20}}$$ $$\Rightarrow$$ Ratio $$\approx$$ 10
20

Answer

10

Answer

10
20

Answer

10
30

Answer

10
40

Atoms & Nuclei

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