1. A gold atom has a mass of 3.287 • 10-25 kg and is at rest. It emits an alpha particle that has a mass of 6.646 • 10-27 kg. In this process, the gold atom is transformed into an iridium isotope. The alpha particle has a speed of 3.40 • 106 m/s.

A. What is the absolute value of the momentum of the alpha particle?
B. What is the absolute value of the momentum of the iridium isotope after the emission of the alpha particle?
C. What is the speed of the iridium isotope after the emission process?

Hint: For the purposes of this problem, assume that the mass of the iridium isotope is simply the difference of the mass of the gold atom and that of the alpha particle.

m₁=6.646•10⁻²⁷ kg, v₁=3.4•10⁶ m/s,

m₂=3.287•10⁻²⁵-6.646•10⁻²⁷=3.22054•10⁻²⁵ kg,
v₂=?

p₁=m₁v₁=6.646•10⁻²⁷•3.4•10⁶=2.25964•10⁻²⁰ kg•m/s
The law of conservation of linear momentum
0 =m₁v₁-m₂v₂
v₂=m₁v₁/m₂=
=6.646•10⁻²⁷•3.4•10⁶/3.22054•10⁻²⁵=7.02•10⁴ m/s
p₂=m₂v₂=…

Thank you so much!

I got 22.61x10^-21 is that right?

My only question is how to find the speed of the particles

To solve this problem, we need to apply the law of conservation of momentum. According to this law, the total momentum before a collision is equal to the total momentum after the collision, provided there are no external forces acting on the system.

Let's break down the problem step by step:

A. What is the absolute value of the momentum of the alpha particle?

The momentum is defined as the product of an object's mass and its velocity:

momentum = mass * velocity

Given that the mass of the alpha particle is 6.646 * 10^-27 kg and the speed is 3.40 * 10^6 m/s, we can calculate the momentum:

momentum = (6.646 * 10^-27 kg) * (3.40 * 10^6 m/s)

To obtain the absolute value of the momentum, we ignore the direction of the vector quantity. Therefore, the absolute value of the momentum of the alpha particle is:

absolute momentum = |momentum|

B. What is the absolute value of the momentum of the iridium isotope after the emission of the alpha particle?

According to the hint in the problem, the mass of the iridium isotope is the difference between the mass of the gold atom and the alpha particle:

mass of iridium isotope = mass of gold atom - mass of alpha particle

Given that the mass of the gold atom is 3.287 * 10^-25 kg and the mass of the alpha particle is 6.646 * 10^-27 kg, we can calculate the mass of the iridium isotope:

mass of iridium isotope = (3.287 * 10^-25 kg) - (6.646 * 10^-27 kg)

Once we have the mass of the iridium isotope, we can calculate its momentum using the formula momentum = mass * velocity. Again, we take the absolute value:

momentum = (mass of iridium isotope) * (velocity of iridium isotope)

absolute momentum = |momentum|

C. What is the speed of the iridium isotope after the emission process?

To find the speed of the iridium isotope, we need to know its momentum and mass. We already calculated the momentum in the previous step, and we know the mass of the iridium isotope from the hint.

speed = momentum / mass

speed of iridium isotope = absolute momentum / mass of iridium isotope

Now you can plug in the values to calculate the absolute value of the momentum of the alpha particle, the absolute value of the momentum of the iridium isotope, and the speed of the iridium isotope.