Question

Proton , deutron and alpha particles of same kinetic energy are moving in circular trajectories in a constant magnetic field . The radii of proton , deuteron and alpha particle are respectively rₚ ,rd and rₐ . which one of the following relation is correct ? [AIEEE 2012]

(a) rₐ = rₚ = rd

(b) rₐ = rₚ < rd

(c) rₐ> rd > rₚ

(d) r ₐ = rd > rₚ ​

Answer 1

Answer:

B)rₐ = rₚ < rd

Explanation:

hope it helps you

Answer 2

Answer:

Option (B) rₐ = rₚ < rd is correct relation

Explanation:

Given :- Kinetic energy is same for proton , deutron and alpha particles

radii of proton, rₚ

radii of alpha particle , rₐ

radii of deuteron ,rd

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For charged particle in magnetic field , radius

r = mv/qB = √2km/qB

[as mv = p => k = 1/2mv² = m²v² /2m = p² /2m

p = √2Km ]

• => r ∝ √m/q

or , md = 2mₚ , qd = qₚ

mₐ = 4mₚ

and qₐ = 2qₚ

• => rₚ = rd = rₐ = √mₚ /qₚ : √2mₚ/qₚ : √4mₚ /2qₚ
• => rₚ = rd = rₐ = √mₚ /qₚ : √2mₚ/qₚ : √4mₚ /2qₚ = 1: √2 :1

• ∴ rₐ = rₚ < rd Answer

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