Step 1: Find the final velocities after the collision
The first particle has mass
8µg and moves with speed
u1. The second particle has mass
4µg and is at rest, so
u2=0.
The formula for the final speed of the first particle after an elastic, one-dimensional collision is:
v1=‌ Plug in the numbers:
v1=‌=‌=‌The formula for the final speed of the second particle is:
v2=‌ Plug in the numbers:
v2=‌=‌=‌u1Step 2: Find the de-Broglie wavelength for each particle
The de-Broglie wavelength formula is:
λ=‌ where
h is Planck's constant,
m is mass, and
v is velocity.
To compare their wavelengths, find the ratio:
‌=‌Plug in the values found earlier:
‌=‌Simplify the expression:
=‌=‌=‌=‌ So,
‌=2 which means the ratio of their wavelengths after the collision is
2:1
