Point A is at a potential of +270 V, and point B is at a potential of -130 V. An α-particle is a helium nucleus that contains two protons and two neutrons; the neutrons are electrically neutral. An α-particle starts from rest at A and accelerates toward B. When the α-particle arrives at B, what kinetic energy (in electron volts) does it have?
(delta) V=EPE/q
400V = EPE/q
400V*q = Ekfinal (in J)
400V*3.2x10^(-19) (the charge of two protons in helium nucleus) = Ekfinal (in J) = 1.28x10^(-16) J
Convert this to eV (divide by the charge on 1 electron), and you get 800
To find the kinetic energy of an α-particle at point B, we can use the equation for the change in electric potential energy:
ΔPE = q × ΔV
Where:
ΔPE is the change in potential energy
q is the charge of the particle (in this case, the charge of an α-particle is equal to the charge of two protons, since it consists of two protons)
ΔV is the change in electric potential (potential difference)
Given:
Potential at point A, V(A) = +270 V
Potential at point B, V(B) = -130 V
We can calculate the potential difference ΔV:
ΔV = V(B) - V(A)
= -130 V - (+270 V)
= -400 V
Now, we can substitute the values into the equation for ΔPE:
ΔPE = (2e) × ΔV
Where:
e is the elementary charge, which is 1.6 × 10^-19 C
ΔPE = (2 × 1.6 × 10^-19 C) × (-400 V)
= -1.28 × 10^-16 J
To find the kinetic energy K at point B, we know that the total energy of the particle is conserved. Therefore, the kinetic energy at point B is equal to the negative potential energy at point A (since potential energy increases as we move towards higher potential):
K = -ΔPE
= -(-1.28 × 10^-16 J)
= 1.28 × 10^-16 J
Converting this to electron volts (eV):
1 eV = 1.6 × 10^-19 J
K(eV) = (1.28 × 10^-16 J) / (1.6 × 10^-19 J)
= 800 eV
Therefore, the kinetic energy of the α-particle when it arrives at point B is 800 eV.
To calculate the kinetic energy of the α-particle when it arrives at point B, we can use the conservation of energy principle.
The potential energy difference between point A and point B can be calculated by multiplying the charge of the α-particle with the potential difference between the two points:
Potential Energy Difference = q * (V_B - V_A)
Here, q represents the charge of the α-particle, which is equal to twice the charge of a proton (2 * 1.6 x 10^-19 C).
The potential difference between point A and point B is calculated by subtracting the potential at point A from the potential at point B:
V_B - V_A = -130 V - 270 V = -400 V
Substituting these values into the equation, we get:
Potential Energy Difference = (2 * 1.6 x 10^-19 C) * (-400 V)
Next, we can equate the potential energy difference to the kinetic energy gained by the α-particle:
Kinetic Energy = Potential Energy Difference
Finally, we convert the answer to electron volts by using the conversion factor 1 eV = 1.6 x 10^-19 J. Therefore:
Kinetic Energy (in eV) = Potential Energy Difference / (1.6 x 10^-19 J)
By plugging in the values and performing the calculation, we can determine the kinetic energy of the α-particle when it arrives at point B.