Given below are three schematic graphs of potential energy V(r) v… - Vidyadip

MCQ

Given below are three schematic graphs of potential energy $V(r)$ versus distance $r$ for three atomic particles : electron $\left(e^{-}\right)$, proton $\left(p^{+}\right)$and neutron $(n)$, in the presence of a nucleus at the origin $O$. The radius of the nucleus is $r_0$. The scale on the $V$-axis may not be the same for all figures. The correct pairing of each graph with the corresponding atomic particle is

✓
$(1, n),\left(2, p^{+}\right),\left(3, e^{-}\right)$
B
$\left(1, p^{+}\right),\left(2, e^{-}\right),(3, n)$
C
$\left(1, e^{-}\right),\left(2, p^{+}\right),(3, n)$
D
$\left(1, p^{+}\right),(2, n),\left(3, e^{-}\right)$

✓

Answer

Correct option: A.

$(1, n),\left(2, p^{+}\right),\left(3, e^{-}\right)$

a
(a)

For an electron and nucleus pair, Potential energy $=\frac{K(-e)(+Z e)}{r}$

$=\frac{-K Z e^2}{r}$

So, potential energy of electron is negative and it tends to zero as separation $r$ increases.

Hence, correct variation of potential energy with $r$ is as shown in graph $(3)$. For a neutron, force outside nucleus is zero.

Hence, potential energy of neutron is zero as $r > r_0$.

So, correct variation of potential energy with $r$ for a neutron is as shown in graph $(1)$.

For a proton, as $r > r_0$, force is repulsive. Hence, potential energy is positive.

So, correct variation of potential energy with $r$ is as shown in graph $(2)$.

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