alpha particles are accelerated through a potential of 1000volts and then enter a magnetic field 0.2T perpendicular to the their direction of motion.Calculate the radius of the circular path that they traverse.An alpha particle has a mass 6.68x 10^-27kg and a charge of +2e.
To calculate the radius of the circular path that the alpha particles traverse, we need to use the formula for the radius of a charged particle moving in a magnetic field.
The formula is given by:
r = (m * v) / (q * B)
Where:
r = radius of the circular path
m = mass of the alpha particle
v = velocity of the alpha particle
q = charge of the alpha particle
B = magnetic field strength
First, we need to find the velocity of the alpha particle. We can use the equation for kinetic energy:
KE = q * V
Where:
KE = kinetic energy
q = charge of the alpha particle
V = potential difference
Now, let's calculate the velocity:
V = 1000 volts (given)
q = +2e (charge of the alpha particle, e = elementary charge = 1.6 × 10^-19 Coulombs)
KE = q * V
= (2e) * 1000 volts
= 2 * 1.6 × 10^-19 C * 1000 volts
= 3.2 × 10^-16 C * V
Since kinetic energy (KE) is given by the formula:
KE = (1/2) * m * v^2
We can set the equation equal to KE, solve for v:
(1/2) * m * v^2 = 3.2 × 10^-16 C * V
Now, solve for v:
v^2 = (2 * 3.2 × 10^-16 C * V) / m
v = sqrt((2 * 3.2 × 10^-16 C * V) / m)
Now, calculate the value of v using the given values:
m = 6.68 × 10^-27 kg (mass of the alpha particle)
v = sqrt((2 * 3.2 × 10^-16 C * 1000 V) / (6.68 × 10^-27 kg))
Once we have the value for v, we can use it to calculate the radius (r) of the circular path:
r = (m * v) / (q * B)
Given:
B = 0.2 T (magnetic field strength)
q = +2e (charge of the alpha particle)
m = 6.68 × 10^-27 kg (mass of the alpha particle)
v = sqrt((2 * 3.2 × 10^-16 C * 1000 V) / (6.68 × 10^-27 kg))
Plugging these values into the equation, we can calculate the radius (r) of the circular path that the alpha particles traverse.