Respuesta :
Answer:
[tex]\sqrt{ \frac{2.3 *10^{-28} }{F} }[/tex]
Explanation:
Total force = Force due to gravity + Force due to charges
Total force = [tex]\frac{GMm}{r^{2} } + \frac{kQq}{r^{2} }[/tex]
r is the separation between particles.
Charge of a proton(Q) = - (charge of an electron(q) ) = 1.6 * 10^-19 coulombs
Mass of a proton (M)= 1.67×10^-27 kilograms
Mass of an electron (m) =9.11 × 10^-31 kilograms
G=6.67 ×10^−11 N⋅m^2/kg^2
k=8.99 * 10 ^9 N.m^2 / C^2
Plugging in values:
Force due to gravity= (6.67 *10^−11)(1.67 * 10^-27)*(9.11 * 10^-31) /r^2 =1.01 * 10^-67 / r^2
Force due to charges : (8.99 * 10 ^9)*(1.6 * 10^-19)*(1.6 * 10^-19) / r^2 = 2.3 *10^-28 / r^2
We can observe that force due to charges is too large as compared with force due to charge. The ratio of Fc to Fm is 2.3* 10^39. It means that we can ignore force due to gravity.
Total force = Force due to charges.
F = 2.3 *10^-28 / r^2
r = [tex]\sqrt{ \frac{2.3 *10^{-28} }{F} }[/tex]
The subatomic positive and negatively charged particles in the atom is called proton and electron. The protons are found in the nucleus of the atom while the electrons are found in the orbits surrounding the nuclei.
[tex]\sqrt{\dfrac{2.3 \times 10^{-28}}{\rm F}}[/tex] is the distance between the electron and proton.
The distance can be estimated as:
The total force is equivalent to the forces of gravity and charges and can be given as,
Total force = [tex]\dfrac{\rm GMm}{\rm r^{2}} + \dfrac{\rm kQq}{\rm r^{2}}[/tex]
Where r = distance between the two particles.
- Charge of a proton(Q) = - (charge of an electron(q) )
[tex]= 1.6 \times 10^{-19} \rm coulombs[/tex]
- Mass of a proton (M) = [tex]1.67 \times 10^{-27} \rm kilograms[/tex]
- Mass of an electron (m) = [tex]9.11 \times 10^{-31} \rm kilograms[/tex]
- G = [tex]6.67 \times 10^{-11} \rm Nm^{2}/kg^{2}[/tex]
- k = [tex]8.99 \times 10 ^{9} \rm Nm^{2} / C^{2}[/tex]
Substituting values:
- Force due to gravity:
[tex]\begin{aligned}&= \dfrac{(6.67 \times 10^{-11})(1.67 \times 10^{-27}) \times (9.11 \times 10^{-31}) }{\rm r^{2}} \\\\&=\dfrac{1.01 \times 10^{-67} }{\rm r^{2}}\end{aligned}[/tex]
- Force due to charges:
[tex]\begin{aligned} & = \dfrac{(8.99 \times 10 ^{9}) \times (1.6 \times 10^{-19}) \times (1.6 \times 10^{-19}) }{\rm r^{2}} \\&= \dfrac{2.3 \times 10^{-28} }{\rm r^{2}}\end{aligned}[/tex]
The proportionate of the force of charge to Fm is [tex]2.3 \times 10^{39}[/tex]. Hence, the force of gravity can be ignored.
Total force will be equivalent to the force exerted by the charges.
[tex]\rm F = \dfrac{2.3 \times 10^{-28} }{r^{2}}[/tex]
[tex]\rm r = \sqrt{\dfrac{2.3 \times 10^{-28}}{\rm F}}[/tex]
Therefore, distance will be [tex]\sqrt{\dfrac{2.3 \times 10^{-28}}{\rm F}}[/tex].
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