Question

Протон і альфа частинка , які мають однакове значення кінетичної енергії влітають в однорідне магнітне поле перпендикулярно до ліній магнітної індукції. У скільки разів відрізняються радіуси їх траєкторій ?

Answer 1

Bvq=mv^2/R
когда перпендикулярны, то сила кулона=силе центростремительной
R=mv/Bq
масса а-частицы в 4 раза больше
заряд в 2 раза
Ra/Rp=4mv/B2q * Bq/mv=2

Answer 2

Proton and Alpha Particle Trajectories in a Magnetic Field

When a proton and an alpha particle with the same kinetic energy enter a homogeneous magnetic field perpendicular to the magnetic field lines, their trajectories will differ due to their different masses and charges.

The radius of the trajectory for a charged particle moving in a magnetic field is given by the formula:

r = (m*v)/(q*B)

Where: - r = radius of the trajectory - m = mass of the particle - v = velocity of the particle - q = charge of the particle - B = magnetic field strength

The kinetic energy of a particle is given by the formula:

KE = (1/2)mv^2

Comparison of Proton and Alpha Particle Trajectories

1. Proton: - Mass (m): 1.67 x 10^-27 kg - Charge (q): 1.6 x 10^-19 C - Kinetic Energy (KE): Given - Velocity (v): Can be calculated using the given kinetic energy and mass

2. Alpha Particle: - Mass (m): 6.64 x 10^-27 kg - Charge (q): 3.2 x 10^-19 C - Kinetic Energy (KE): Given - Velocity (v): Can be calculated using the given kinetic energy and mass

By plugging the values into the formula for the radius of the trajectory, we can calculate the ratio of the radii of their trajectories.

Let's calculate the velocities of the proton and alpha particle using their kinetic energies and masses, and then compare the radii of their trajectories.