A proton and an α -particle, having kinetic energies K p and K α , respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that of α -particle is 2 : 1 . The ratio of K

Question

A proton and an &#945; -particle, having kinetic energies K p and K &#945; , respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that of &#945; -particle is 2 : 1 . The ratio of K p : K &#945; is:

Quantrex Academy · Accepted Answer

Correct answer: D. 4 : 1

r = m v q B = p q B &#160;&#160; m &#945; m p = 4 r p r &#945; = p p q p q &#945; p &#945; = 2 1 p p p a = 2 q p q a = 2 1 2 p p p &#945; = 1 K p K &#945; = p p 2 p &#945; p m &#945; m p = 1 4

A proton and an α -particle, having kinetic energies K p and K α , respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that of α -particle is 2 : 1 . The ratio of K p : K α is:

Options

Correct answer

Step-by-step solution

More from Magnetic Effects of Current

A proton and an &#945; -particle, having kinetic energies K p and K &#945; , respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that of &#945; -particle is 2 : 1 . The ratio of K p : K &#945; is:

Options

Correct answer

Step-by-step solution

More from Magnetic Effects of Current

A proton and an α -particle, having kinetic energies K p and K α , respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that of α -particle is 2 : 1 . The ratio of K p : K α is: