A uranium nucleus (mass 238 units) at rest decays into a helium nucleus (mass 4.0 units) and a thorium nucleus (mass 234 units). If the speed of the helium nucleus is 6.5 × 105 m/s, what is the speed of the thorium nucleus?Select one:a.1,440.0 × 104 m/sb.3,802.5 × 104 m/sc.​0.1 × 104 m/sd.1.1 × 104 m/se.2.1 × 104 m/s

This problem can be solved using the principle of conservation of momentum. The total momentum before the decay is equal to the total momentum after the decay.

Before the decay, the total momentum is zero because the uranium nucleus is at rest.

After the decay, the total momentum is the sum of the momenta of the helium and thorium nuclei. The momentum of an object is given by its mass times its velocity.

Let's denote the speed of the thorium nucleus as v. The momentum of the helium nucleus is its mass times its velocity, or (4.0 units)(6.5 × 10^5 m/s). The momentum of the thorium nucleus is its mass times its velocity, or (234 units)(v).

Setting the total momentum before the decay equal to the total momentum after the decay gives:

0 = (4.0 units)(6.5 × 10^5 m/s) + (234 units)(v)

Solving this equation for v gives:

v = - (4.0 units)(6.5 × 10^5 m/s) / (234 units)

v = - (2.6 × 10^6 units*m/s) / (234 units)

v = -1.1 × 10^4 m/s

The negative sign indicates that the thorium nucleus is moving in the opposite direction of the helium nucleus. However, since the problem asks for the speed of the thorium nucleus, we take the absolute value of v.

So, the speed of the thorium nucleus is 1.1 × 10^4 m/s.

Therefore, the correct answer is d. 1.1 × 10^4 m/s.