If a proton is accelerated from rest through a potential difference of 1500 V, find its final velocity. proton mass = 1.67 x10−27 kg
Handheld
KE=Work done
1/2 m v^2=1500*chargeonaproton
To find the final velocity of a proton accelerated through a potential difference, we can use the principles of energy conservation.
The potential difference (V) is given as 1500 V, and the mass of the proton (m) is given as 1.67 × 10^(-27) kg.
1. First, we need to calculate the change in potential energy (ΔPE) of the proton using the formula:
ΔPE = q × V
Since the proton has a charge (q) of +1.6 × 10^(-19) C, and the potential difference (V) is given as 1500 V, we can substitute the values:
ΔPE = (1.6 × 10^(-19) C) × (1500 V)
2. Next, we know that the change in potential energy is equal to the change in kinetic energy (ΔKE) of the proton:
ΔKE = ΔPE
3. The change in kinetic energy is given by the formula:
ΔKE = (1/2) × m × (vf^2 - vi^2)
Since the proton starts from rest, the initial velocity (vi) is 0. Therefore, the equation simplifies to:
ΔKE = (1/2) × m × vf^2
Rearranging the equation, we get:
vf^2 = (2 × ΔKE) / m
4. Substituting the value of ΔKE from step 1 and the mass of the proton (m) into the equation, we can solve for vf:
vf^2 = (2 × (1.6 × 10^(-19) C × 1500 V)) / (1.67 × 10^(-27) kg)
5. Simplifying the equation, we find:
vf^2 = (4.8 × 10^(-17) kg⋅C⋅V) / (1.67 × 10^(-27) kg)
6. Calculating vf, we take the square root of both sides of the equation:
vf = √[(4.8 × 10^(-17) kg⋅C⋅V) / (1.67 × 10^(-27) kg)]
7. Evaluating the expression:
vf ≈ 2.18 × 10^6 m/s
Therefore, the final velocity of the proton after being accelerated through a potential difference of 1500 V is approximately 2.18 × 10^6 m/s.
To find the final velocity of a proton accelerated through a potential difference, we can use the concept of energy conservation. The proton will gain kinetic energy as it moves through the potential difference.
The potential difference (V) is given as 1500 V.
Now, we can calculate the final velocity of the proton using the following steps:
1. The potential difference (V) is the electrical potential energy (E) gained by the proton per unit charge (q). Since the proton has unit charge (q = 1.6 x 10^-19 C), we can calculate the electrical potential energy gained by the proton:
E = q * V
E = (1.6 x 10^-19 C) * (1500 V)
2. The electrical potential energy gained by the proton is converted into its kinetic energy (K) as it accelerates. The kinetic energy of an object with mass (m) and velocity (v) is given by:
K = (1/2) * m * v^2
3. Equating the electrical potential energy gained by the proton to its final kinetic energy, we can set up the following equation:
E = K
(1.6 x 10^-19 C) * (1500 V) = (1/2) * (1.67 x 10^-27 kg) * v^2
4. Solve the equation for 'v' by rearranging it:
v^2 = ((1.6 x 10^-19 C) * (1500 V) * 2) / (1.67 x 10^-27 kg)
v^2 = (4.8 x 10^-16 m^2/s^2) / (1.67 x 10^-27 kg)
v^2 = 2.875 * 10^11 m^2/s^2
5. Take the square root of both sides of the equation to find 'v':
v ≈ √(2.875 * 10^11 m^2/s^2)
v ≈ 5.36 x 10^5 m/s
Therefore, the final velocity of the proton is approximately 5.36 x 10^5 m/s.