A proton, a deuteron and an α -particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energies. The ratio of the radii of the circular paths described by them is

Question

A proton, a deuteron and an α -particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energies. The ratio of the radii of the circular paths described by them is (A) 1:√2:1 (B) 1:√2:√2 (C) √2:√2:1 (D) √2:1:1

Tardigrade Admin · Accepted Answer

According to the question, magnetic field is uniform and the kinetic energy for each particle is same.
We know that,

r = \frac{m v}{qB} = \frac{2 m ( K . E . )}{qB}

r \propto \frac{m}{q}

r_{p} : r_{d} : r_{α} = \frac{1}{1} : \frac{2}{1} : \frac{4}{2}

= 1 : 2 : 1

Q. A proton, a deuteron and an $α$ -particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energies. The ratio of the radii of the circular paths described by them is

$1 : 2 : 1$

$1 : 2 : 2$

$2 : 2 : 1$

$2 : 1 : 1$

According to the question, magnetic field is uniform and the kinetic energy for each particle is same.
We know that,
$r = \frac{m v}{qB} = \frac{2 m ( K . E . )}{qB}$
$r \propto \frac{m}{q}$
$r_{p} : r_{d} : r_{α} = \frac{1}{1} : \frac{2}{1} : \frac{4}{2}$
$= 1 : 2 : 1$

Q. A proton, a deuteron and an α -particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energies. The ratio of the radii of the circular paths described by them is

1:2​:1

1:2​:2​

2​:2​:1

2​:1:1