Question

An alpha nucleus of energy `1/2`mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to ______.

1. v²
2. `1/"m"`
3. `1/"v"^2`
4. `1/"Ze"`

Answer 1

An alpha nucleus of energy `1/2`mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be both proportional to `bb(1/"m"  "and"1/"v"^2)`.

Explanation:

work done to stop the α particle is equal to K.E.

∴ qV = `1/2`mv²

⇒ `"q"xx("K"("Ze"))/"r" = 1/2 "mv"^2`

⇒ r = `(2(2"e")"K"("Ze"))/"mv"^2 = (4"KZe"^2)/"mv"^2`

⇒ r ∝ `1/"v"^2` r ∝ `1/"m"`