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 find the radius of the circular path that the alpha particles traverse, we can use the principles of circular motion and apply the Lorentz force equation.
The Lorentz force equation is given by: F = q(v x B), where F is the force experienced by the charged particle, q is the charge of the particle, v is the velocity of the particle, and B is the magnetic field.
In this case, we need to calculate the radius of the circular path, which can be achieved by balancing the Lorentz force with the force of centripetal acceleration.
The centripetal force acting on the charged particle is given by: F_c = (mv^2) / r, where m is the mass of the particle, v is the velocity, and r is the radius of the circular path.
Equating the Lorentz force (F = q(v x B)) with the centripetal force (F_c = (mv^2) / r), we get:
qvB = (mv^2) / r
Simplifying the equation, we can solve for the radius (r):
r = (mv) / (qB)
Given information:
Charge of an alpha particle, q = +2e, where e is the elementary charge
Mass of an alpha particle, m = 6.68 × 10^(-27) kg
Potential difference (accelerating potential), V = 1000 V
Magnetic field, B = 0.2 T
To calculate the velocity (v) of the alpha particle, we can use the relationship between kinetic energy (K.E.) and potential energy (P.E.):
K.E. = P.E.
(1/2)mv^2 = qV
v^2 = (2qV) / m
v = √((2qV) / m)
Substituting the given values, we have:
v = √((2 * (2 * 1.6 × 10^(-19) C) * (1000 V)) / (6.68 × 10^(-27) kg))
Calculating the velocity (v), we find:
v ≈ 2.19 × 10^6 m/s
Now we can substitute the values of v, q, m, and B into the radius equation:
r = ((6.68 × 10^(-27) kg) * (2.19 × 10^6 m/s)) / ((2 * 1.6 × 10^(-19) C) * (0.2 T))
Calculating the radius (r), we find:
r ≈ 1.663 meters
Therefore, the radius of the circular path traversed by the alpha particles is approximately 1.663 meters.