Question

Suppose the charge of a proton and electron differ slightly. One of them is\[ - e\], the other is\[(e + \Delta e)\]. If the net of electrostatic force and the gravitational force between two hydrogen atoms placed at a distance (much greater than atomic size ) apart is zero, then \[\Delta e\]is of the order of [Given mass of hydrogen \[{m_h}\]\[ = 1.67 \times {10^{ - 27}}\]\[Kg\]].
$(A)$ \[{10^{ - 47}}\]\[C\]
$(B)$ \[{10^{ - 20}}\]\[C\]
$(C)$ \[{10^{ - 23}}\]\[C\]
$(D)$ \[{10^{ - 37}}\]\[C\]

Answer 1

Hint: Gravitational force is corresponding to the majority of collaborating objects, and the electrostatic force is relative to the extent of the charges of associating objects. Subsequently, both forces are relative to a property that speaks to the quality of cooperation for a given field. The fundamental distinction between gravitational and electrostatic force is that: Gravitational force is the force by which earth pulls in different items by mass. While electrostatic force is the force of an article because of charge. This paper investigates the thought that gravity is simply a genuinely straight forward utilization of the well known electrostatic power. It is indicated that gravity isn't the mysterious force we think it is. Gravity is essentially the electrostatic power.

Complete step by step answer:
Given:
 \[mh = 1.67 \times {10^{ - 27}}Kg\]
The net charge on the hydrogen atom \[q = (e + \Delta e) - e\]
 \[ = \Delta e\]
 Let the distance then be \[d\]
Equating gravitational force and the electrostatic force we get
 \[\dfrac{{G{m^2}h}}{{{d^2}}} = \dfrac{{K{{(\Delta e)}^2}}}{{{d^2}}}\]
 Cancel out \[{d^2}\]on both sides, and
 Substitute the values of \[G\] and given mass of hydrogen atom
 \[\Rightarrow \dfrac{{(6.67 \times {{10}^{ - 11}}){{(1.67 \times {{10}^{ - 27}})}^2}}}{{{d^2}}} = \dfrac{{(9 \times {{10}^9}){{(\Delta e)}^2}}}{{{d^2}}}\]
 \[ \therefore \Delta e = 2.06 \times 1{0^{ - 37}}C\]
 Hence the correct option is \[(D)\].

Note: Gravitational power is corresponding to the majority of collaborating objects, and the electrostatic power is relative to the extents of the charges of interfacing objects. Subsequently, the two powers are relative to a property that speaks to the quality of cooperation for a given field. In electrostatic power, the power of medium relies upon charges while the power of medium because of gravity doesn't rely upon masses.