An electron accelerated from rest through a potential difference of 50v acquires a speed of 4.2x10^6m/s write down the speed that a potential difference of 200v would produce ?
To find the speed that a potential difference of 200V would produce for an electron, we can use the relationship between potential difference and kinetic energy.
The kinetic energy of the electron can be calculated using the formula:
K.E. = (1/2)mv^2
where K.E. is the kinetic energy, m is the mass of the electron, and v is the speed of the electron.
Given that the initial speed of the electron is 0 m/s, the kinetic energy acquired is equal to the work done on the electron by the potential difference. Therefore, we can write:
K.E. = qV
where q is the charge of the electron and V is the potential difference.
Since the charge of an electron is -1.6 x 10^-19 C, we can now calculate the initial kinetic energy (K.E1) acquired by the electron when accelerated through a potential difference of 50V:
K.E1 = (-1.6 x 10^-19 C)(50V)
Next, we can use the principle of conservation of energy to find the kinetic energy (K.E2) acquired when the electron is accelerated through a potential difference of 200V:
K.E1 = K.E2
(-1.6 x 10^-19 C)(50V) = (-1.6 x 10^-19 C)(200V)
Simplifying the equation, we find:
(-1.6 x 10^-19 C)(50V) = (-1.6 x 10^-19 C)(200V)
-80 x 10^-19 C = -320 x 10^-19 C
Since the charge on both sides of the equation is the same, we can equate the magnitudes of the kinetic energies and find:
80 x 10^-19 C = 320 x 10^-19 C
Dividing both sides of the equation by (-1.6 x 10^-19 C) to solve for V2:
V2 = [320 x 10^-19 C]/[-1.6 x 10^-19 C]
V2 = -200V
The negative sign indicates that the direction of the velocity of the electron is opposite to the direction of the electric field. Therefore, the speed that a potential difference of 200V would produce for the electron is also 4.2 x 10^6 m/s.
To determine the speed that a potential difference of 200V would produce, we need to understand the relationship between potential difference and the speed of an electron.
The kinetic energy of an electron can be calculated using the following formula:
KE = (1/2)mv^2
Where:
KE = Kinetic energy of the electron
m = Mass of the electron
v = Velocity of the electron
The potential difference (V) can be related to the kinetic energy (KE) using the equation:
KE = qV
Where:
q = Charge of an electron (which is given as -1.6 x 10^-19 C)
V = Potential difference
In this case, we can set up the following equation to find the speed:
KE₁ = KE₂
qV₁ = (1/2)mv₁² = (1/2)m(4.2 x 10⁶ m/s)² [Using the given values]
Now, we can solve for v₂ when V₂ = 200V:
qV₂ = (1/2)m(v₂)²
Substituting the known values:
(-1.6 x 10^-19 C)(200V) = (1/2)m(v₂)²
Now, we can solve for v₂:
v₂² = (-1.6 x 10^-19 C)(200V) / (1/2)m
v₂ = √[(-1.6 x 10^-19 C)(200V) / (1/2)m]
To calculate the actual value, we need the mass of the electron (m) in kilograms. The mass of an electron is approximately 9.11 x 10^-31 kg.
Now, substitute the values into the formula and evaluate:
v₂ = √[(-1.6 x 10^-19 C)(200V) / (1/2)(9.11 x 10^-31 kg)]
By plugging in the values and simplifying the equation, you can find the speed that a potential difference of 200V would produce.
velocity^2 = k*energy
you increase the energy by (200/50)^2=4
so speed doubles.