Question 247: Atoms & Nuclei

Question

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its
energy is p
d
; while for its similar collision with carbon nucleus at rest, fractional loss of energy is p
c
. The values of p
d
and p
c
are respectively :

Accepted Answer

Applying conservation of momentum :
mv + 0 = mv
1
+ 2mv
2
$$ \Rightarrow $$$$\,\,\,$$ v = v
1
+ 2v
2
. . . . . (1)
As collision is elastic,
So, coefficient of restitution, e = 1
$$	herefore\,\,\,$$ e = 1 = $${{velocity\,\,of\,\,separation} \over {Velocity\,\,of\,\,approach}}$$
$$ \Rightarrow $$$$\,\,\,$$ 1 = $${{{v_2} - {v_1}} \over {v - 0}}$$
$$ \Rightarrow $$$$\,\,\,$$ v = v
2
$$-$$ v
1
. . . . .(2)
Add (1) and (2),
2v = 3v
2
$$ \Rightarrow $$$$\,\,\,$$ v
2
= $${{2v} \over 3}$$
put value of v
2
in equation (1),
v
1
= v $$-$$ 2v
2
= v $$-$$ $${{4v} \over 3}$$
= $$-$$ $${v \over 3}$$
$$	herefore\,\,\,$$ Fractional loss of energy of neutron.
P
d
= $${{{k_i} - {k_f}} \over {{k_i}}}$$
= $${{{1 \over 2}m{v^2} - {1 \over 2}mv_1^2} \over {{1 \over 2}m{v^2}}}$$
= $${{{v^2} - {{{v^2}} \over 9}} \over {{v^2}}}$$
= $${8 \over 9}$$
= 0.89
Applying momentum of conservation,
mv + 0 = mv
1
+ 12mv
2
$$ \Rightarrow $$$$\,\,\,$$ v = v
1
+ 12v
2
. . . . . (3)
Here also e = 1
$$	herefore\,\,\,$$ e = 1 =  $${{{v_2} - v{}_1} \over {v - 0}}$$
$$ \Rightarrow $$$$\,\,\,$$ v = v
2
$$-$$ v
1
. . . . . . (4)
adding (3) and (4), we get
2v = 13v
2
$$ \Rightarrow $$$$\,\,\,$$ v
2
= $${{2v} \over {13}}$$
put this v
2
in equation (3), we get
v
1
= v $$-$$ 12 $$ 	imes $$ $${{2v} \over {13}}$$
= $$-$$ $${{11v} \over {13}}$$
$$	herefore\,\,\,$$ Frictional loss
p
c
= $${{{1 \over 2}m{v^2} - {1 \over 2}m{{\left( {{{11} \over {13}}v} ight)}^2}} \over {{1 \over 2}m{v^2}}}$$
= $${{48} \over {169}}$$
= 0.28

Answer

(0, 1)

Answer

(0.89, 0.28)

Answer

(0.28, 0.89)

Answer

(0, 0)

Atoms & Nuclei

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is p d ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is p c . The values of p d and p c are respectively :

Choose the correct answer: