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Atoms and Nuclei question

2020 · 3 Sep · Shift 2 · Q46

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Atoms and Nuclei
2020 · 3 Sep · Shift 2 · Q46

Atoms and Nuclei question

2020 · 3 Sep · Shift 2 · Q46

JEE MainPhysicsAtoms and NucleiMCQ+4 / −1

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to :

A
2 : 1
B
1 : 2
C
5 : 7
D
10 : 7

View written solutionFree

Correct answer: A

Use energy gained from accelerating potential

When a charged particle of charge $q$ is accelerated from rest through a potential difference $V$ , the gained kinetic energy is:

$qV = \frac{1}{2}mv^2$

So,

$v = \sqrt{\frac{2qV}{m}}$

Thus, for the same potential difference $V$ ,

$v \propto \sqrt{\frac{q}{m}}$

For hydrogen ion

A hydrogen ion is essentially a proton:

charge $= +e$
mass $\approx m_p$

Hence,

$v_H = \sqrt{\frac{2eV}{m_p}}$

For singly ionized helium atom

A singly ionized helium atom is $\text{He}^+$ :

charge $= +e$
mass $\approx 4m_p$

Hence,

$v_{He} = \sqrt{\frac{2eV}{4m_p}} = \frac{1}{2}\sqrt{\frac{2eV}{m_p}}$

So,

$v_{He} = \frac{v_H}{2}$

Find the ratio

$v_H : v_{He} = 2 : 1$

Check options

A: $2:1$ ✅
B: $1:2$ ❌
C: $5:7$ ❌
D: $10:7$ ❌

Therefore, the correct answer is A.

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