Question

A cyclotron particle accelerator (sometimes called an “atom smasher” in the popular press) is a device for accelerating charged particles, such as electrons and protons, to speeds close to the speed of light. The basic design is quite simple. The particle is bent in a circular path by a uniform magnetic field. An electric field is pulsed periodically to increase the speed of the particle. .The largest cyclotron in the United States is the Tevatron at Fermilab, near Chicago, Illinois. It is called a Tevatron because it can accelerate particles to energies in the TeV range (1.00 tera −eV = 1.00×1012 eV ). Its circumference is 6.40 km , and it currently can produce a maximum energy of 2.00 TeV . In a certain medical experiment on the Tevatron, protons will be accelerated to energies of 1.25 MeV and aimed at a tumor to destroy its cells. How fast are these protons moving when they hit the tumor?

Answer 1

Answer:

$v=1.54\times 10^{7}}\ \textup{m/s}$

Explanation:

Given:

The accelerated energy, U = 1.25 MeV = 1.25 × 10⁶ eV

we know,

1 eV = 1.6 × 10⁻¹⁹ J

thus,

1.25 eV = (1.6 × 10⁻¹⁹) × (1.25) J = 2 × 10⁻¹³ J

Now, Applying the law of conservation of energy, the energy due to acceleration will be equal to the kinetic energy

mathematically,

K.E = U

$\frac{1}{2}mv^2=2\times 10^{-13} \ \textup{J}$

where,

m = mass of the particle = 1.67 × 10⁻²⁷ kg

v = velocity of the particle

on substituting the values we get

$\frac{1}{2}\times 1.67\times 10^{-27}\times v^2=2\times 10^{-13} \ \textup{J}$

or

$v^2=\frac{2\times 10^{-13}}{1.67\times 10^{-27}}$

or

$v=\sqrt{2.39\times 10^{14}}$

or

$v=1.54\times 10^{7}}\ \textup{m/s}$