Respuesta :
Explanation:
It is given that,
The electric potential at point A, [tex]V_A=14.1\ V[/tex]
The electric potential at point B, [tex]V_B=-28.5\ V[/tex]
We know that the relationship between the particle's electrostatic potential energy and the electric potential is given by :
[tex]U=\Delta V\times q[/tex]
q is the charge
U is the electrostatic potential energy
For an electron, [tex]q_e=-1.6\times 10^{-19}\ C[/tex]
For a proton, [tex]q_p=1.6\times 10^{-19}\ C[/tex]
Change in electric potential,
[tex]\Delta V=V_B-V_A[/tex]
[tex]\Delta V=-28.5-14.1=-42.6\ V[/tex]
Electrostatic potential energy for an electron is :
[tex]U=-42.6\times (-1.6\times 10^{-19})[/tex]
[tex]U=6.81\times 10^{-18}\ J[/tex]
Electrostatic potential energy for a proton is :
[tex]U=-42.6\times (1.6\times 10^{-19})[/tex]
[tex]U=-6.81\times 10^{-18}\ J[/tex]
Electrostatic potential energy for a neutral hydrogen atom (q = 0) is :
U = 0
Electrostatic potential energy for a singly ionized helium atom is same as the proton.
The electrostatic potential energy for:
electron = [tex]6.81\times 10^{-18}J[/tex]
proton = [tex]-6.81\times 10^{-18}J[/tex]
Hydrogen atom = 0
Singly ionized Helium atom = [tex]-6.81\times 10^{-18}J[/tex]
According to the question:
let the electric potential at point A be [tex]V_A=14.1V[/tex]
and at point B be [tex]V_B=-28.5V[/tex]
The potential difference between the points B and A is(since we are bringing the charge from point A to B):
[tex]\triangle V=V_B-V_A\\\\\triangle V=28.5-14.1V\\\\\triangle V=-42.6V[/tex]
Now the potential energy U is given by:
U = ΔV×q
where q is the charge of the particle.
(i) for electron [tex]q=-1.6\times 10^{-19}C[/tex]
so,
[tex]U=-42.6\times (-1.6\times 10^{-19})J\\\\U=6.81\times 10^{-18}J[/tex]
(ii) for proton [tex]q=1.6\times 10^{-19}C[/tex]
[tex]U=42.6\times (-1.6\times 10^{-19})J\\\\U=-6.81\times 10^{-18}J[/tex]
(iii)for neutral Hydrogen atom q=0
so, U = 0
(iv) Singly ionized Helium atom has charge same as a proton [tex]q=1.6\times 10^{-19}C[/tex]
therefore, [tex]U=-6.81\times 10^{-18}J[/tex]
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