Answer to Question #86983 in Physics for Maria

Question

A neon atom (m=20.0u) makes a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away at a 18.4 ∘ angle from its original direction and the unknown atom travels away at a -69.2 ∘ angle.

What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.]

Answer 1

From the conservation of momentum:

$$m\vec{u}=m\vec{u'}+M\vec{v}$$

Lets use the law of sines

$$\frac{mu'}{\sin{69.2}}=\frac{Mv}{\sin{18.4}}=\frac{mu}{\sin{(180-69.2-18.4)}}$$

$$v=6.319uM^{-1}$$ $$u'=0.9356u$$

From the conservation of energy:

$$0.5mu^2=0.5mu'^2+0.5MV^2$$

$$0.5(20)u^2=0.5(20)(0.9356u)^2+0.5M(6.319uM^{-1})^2$$

$$M=16.0 u.$$