(a) What is the electric potential V at a distance r = 3.1 10-8 cm from a proton? (V)
(b) What is the electric potential energy in units J and eV of an electron at the given distance from the proton? (J) (eV)
To calculate the electric potential (V) at a distance r from a proton, we can use the equation:
V = k * q / r
where V is the electric potential, k is Coulomb's constant (9.0 x 10^9 Nm^2/C^2), q is the charge of the proton (1.6 x 10^-19 C), and r is the distance from the proton.
Given r = 3.1 x 10^-8 cm, we need to convert it to meters:
r = 3.1 x 10^-8 cm = 3.1 x 10^-10 m
Now we can substitute these values into the equation:
V = (9.0 x 10^9 Nm^2/C^2) * (1.6 x 10^-19 C) / (3.1 x 10^-10 m)
Calculating this expression, we find:
V ≈ 521.62 V
Therefore, the electric potential at a distance of r = 3.1 x 10^-8 cm from a proton is approximately 521.62 V.
To calculate the electric potential energy in joules (J) and electron volts (eV) of an electron at this distance from the proton, we can use the equation:
E = q * V
where E is the electric potential energy, q is the charge of the electron (-1.6 x 10^-19 C), and V is the electric potential (521.62 V).
Substituting the values into the equation, we get:
E = (-1.6 x 10^-19 C) * (521.62 V)
Calculating this expression, we find:
E ≈ -8.346 x 10^-17 J
To convert the electric potential energy to electron volts, we can use the conversion factor:
1 eV = 1.6 x 10^-19 J
Dividing the energy in joules by this conversion factor, we get:
E (eV) = (-8.346 x 10^-17 J) / (1.6 x 10^-19 J/eV)
Calculating this expression, we find:
E (eV) ≈ -521.63 eV
Therefore, the electric potential energy in joules of an electron at a distance of r = 3.1 x 10^-8 cm from the proton is approximately -8.346 x 10^-17 J, and in electron volts, it is approximately -521.63 eV.
To calculate the electric potential at a certain distance from a point charge, such as a proton, you can use the formula:
V = k*q/r
Where V is the electric potential, k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), q is the charge of the point source (in this case, the charge of a proton is q = 1.6 x 10^-19 C), and r is the distance from the point charge (given as r = 3.1 x 10^-8 cm = 3.1 x 10^-10 m).
Let's calculate the electric potential:
(a) V = (8.99 x 10^9 N m^2/C^2) * (1.6 x 10^-19 C) / (3.1 x 10^-10 m)
Using a calculator, we get:
V ≈ 7.45 x 10^6 V (volts)
To calculate the electric potential energy, we use the formula:
U = q * V
Where U is the electric potential energy, q is the charge of the particle (e.g., the charge of an electron is q = -1.6 x 10^-19 C in this case), and V is the electric potential (which we calculated as V ≈ 7.45 x 10^6 V).
(b) U = (-1.6 x 10^-19 C) * (7.45 x 10^6 V)
Using a calculator, we get:
U ≈ -1.19 x 10^-12 J (joules)
To convert this energy to electron volts (eV), we use the conversion factor: 1 eV = 1.6 x 10^-19 J.
To convert to eV, we divide the energy in joules by the conversion factor:
U (eV) = -1.19 x 10^-12 J / (1.6 x 10^-19 J/eV)
Using a calculator, we get:
U (eV) ≈ -7.44 eV
So, the electric potential energy of the electron at this distance from the proton is approximately -1.19 x 10^-12 J or -7.44 eV.
Why are you asking these? These are standard formula, calculator work.
V=1/4PIeo * Q/r
electric potential energy=1/4PIeo *qQ/r