An α particle passes rapidly through the exact centre of a hydrogen molecule, moving on a line perpendicular to the internuclear axis. The distance between the nuclei is b. Where on its path does the α particle experience the greatest force? (Assume that the nuclei do not move much during the passage of the α particle. Also neglect the electric field of the electrons in the molecule.)

Question

An α particle passes rapidly through the exact centre of a hydrogen molecule, moving on a line perpendicular to the internuclear axis. The distance between the nuclei is b. Where on its path does the α particle experience the greatest force? (Assume that the nuclei do not move much during the passage of the α particle. Also neglect the electric field of the electrons in the molecule.) (A) (b/2) (B) (b/2 √2) (C) (b/√2) (D) None of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/51562ddef46117a40da3c3b86b227512-.png" /> Ep=(2 K ex /(x2+(b2)4)3 / 2) For maximum EP (d EP/d x)=0 ⇒ x=(b/2 √2)

$\frac{b}{2}$

$\frac{b}{2 2}$

$\frac{b}{2}$

None of these

$E_{p} = \frac{2 K _{e x}}{( x ^{2} + \frac{b ^{2}}{4} ) ^{3/2}}$
For maximum $E_{P}$
$\frac{d E _{P}}{d x} = 0 \Rightarrow x = \frac{b}{2 2}$

2b​

22​b​

2​b​

None of these

Ep​=(x2+4b2​)3/22Kex​​ For maximum EP​ dxdEP​​=0⇒x=22​b​

$\frac{b}{2}$

$\frac{b}{2 2}$

$\frac{b}{2}$

$E_{p} = \frac{2 K _{e x}}{( x ^{2} + \frac{b ^{2}}{4} ) ^{3/2}}$
For maximum $E_{P}$
$\frac{d E _{P}}{d x} = 0 \Rightarrow x = \frac{b}{2 2}$