A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let r_d and r_d be their respective radii of circular path. The value of $\frac{r_{d}}{r_{α}}$ is equal to:

Option 1 -

$\sqrt[]{2}$

Option 2 -

Option 3 -

$\frac{1}{\sqrt[]{2}}$

Option 4 -

2 Views | Posted 2 months ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

As we know that radius of circular path in magnetic field is given as $r = \frac{m v}{q B} = \frac{\sqrt[]{2 m K}}{q B}, s o$

$r = \frac{m v}{q B} = \frac{\sqrt[]{2 m K}}{q B}, s o$

$\frac{r_{d}}{r_{α}} = \sqrt[]{\frac{m_{d}}{m_{α}}} \times \frac{q_{α}}{q_{d}} = \frac{1}{\sqrt[]{2}} \times 2 = \sqrt[]{2}$

Charged particle	Charge	Mass
Deuteron	e	2m
Alpha particle	2e	4m

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A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let r_d and r_d be their respective radii of circular path. The value of $\frac{r_{d}}{r_{α}}$ is equal to:

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A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let rd and rd be their respective radii of circular path. The value of r d r α is equal to:

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A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let r_d and r_d be their respective radii of circular path. The value of $\frac{r_{d}}{r_{α}}$ is equal to: