A proton, a deuteron and an alpha particle all having same momenta enter a uniform magnetic field and describe circular paths. The respective radii of their paths are in the ratio

Question

A proton, a deuteron and an alpha particle all having same momenta enter a uniform magnetic field and describe circular paths. The respective radii of their paths are in the ratio (A)  4:2:1  (B)  2:2:1  (C)  1:2:4  (D)  1:1:1

Tardigrade Admin · Accepted Answer

Radius of the path r=(√2 m K/q B) or r propto (√1/q) rp: rd: rα=(√1/qp): (√1/qd): (√1/qα) (1/1): (1/1): (1/2)=2: 2: 1

Q. A proton, a deuteron and an alpha particle all having same momenta enter a uniform magnetic field and describe circular paths. The respective radii of their paths are in the ratio

$4 : 2 : 1$

$2 : 2 : 1$

$1 : 2 : 4$

$1 : 1 : 1$

Radius of the path $r = \frac{2 m K}{qB}$ or $r \propto \frac{1}{q}$
$r_{p} : r_{d} : r_{α} = \frac{1}{q _{p}} : \frac{1}{q _{d}} : \frac{1}{q _{α}}$
$\frac{1}{1} : \frac{1}{1} : \frac{1}{2} = 2 : 2 : 1$

Q. A proton, a deuteron and an alpha particle all having same momenta enter a uniform magnetic field and describe circular paths. The respective radii of their paths are in the ratio

4:2:1

2:2:1

1:2:4

1:1:1

Radius of the path r=qB2​mK​ or r∝q1​​ rp​:rd​:rα​=qp​1​​:qd​1​​:qα​1​​ 11​:11​:21​=2:2:1

$4 : 2 : 1$

$2 : 2 : 1$

$1 : 2 : 4$

$1 : 1 : 1$

Radius of the path $r = \frac{2 m K}{qB}$ or $r \propto \frac{1}{q}$
$r_{p} : r_{d} : r_{α} = \frac{1}{q _{p}} : \frac{1}{q _{d}} : \frac{1}{q _{α}}$
$\frac{1}{1} : \frac{1}{1} : \frac{1}{2} = 2 : 2 : 1$