Question

Ionized hydrogen atoms and α-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths rₕ : rₐ will be :
(1) 2:1
(2) 1:2
(3) 4:1
(4) 1:4

Answer 1

Explanation:

charge on ionized hydrogen atom, q = +e

[ where e = 1.6 × 10^-19C ]

charge on alpha particle , Q = +2e

using formula, r = P/BQ

where P is linear momentum, Q is charge and B is magnetic field.

a/c to question,

linear momentum and magnetic field both are constant.

so, radius of circular path is inversely proportional to charge on it.

i.e., rH/rA = Q/q

= (+2e)/(+e)

= 2/1

hence, answer is 2 : 1

Answer 2

The ratio of their radii of their paths $\bold{r_{H}:r_{\alpha }=2:1}$.

Step by step explanation:

Radii can be calculated by the following formulas.

$\bold{r_{H}=\frac{P}{e\times B}}$

$\bold{r_{\alpha}=\frac{P}{2e\times B}}(\alpha = 2e)$

Let's take the ration of the $r_{H}and\,\,r_{\alpha}$.

$\frac{r_{H}}{r_{\alpha}}=\frac{\frac{P}{eB}}{\frac{P}{2eB}}$

cancel the same constants, then we get

$\frac{r_{H}}{r_{\alpha}}=\frac{2}{1}$

Therefore, the ratio of their radii of their paths is 2:1

Hence, correct option is 1.

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