An unstable particle with a mass equal to 3.34 ✕ 10−27 kg is initially at rest....

An unstable particle with a mass equal to 3.34 ✕ 10⁻²⁷ kg is initially at rest. The particle decays into two fragments that fly off with velocities of 0.976c and −0.862c, respectively. Find the masses of the fragments. (Hint: Conserve both mass–energy and momentum.)

m_(0.976c) =	kg
m_(-0.862c) =kg

Solutions

Expert Solution

Given: The mass of particle, m = 3.34 *10^-27 Kg ; velocity v₁ of fragment 1 = 0.976c ; velocity v₂ of fragment 2 = -0.862c ; speed of light = 3 *10⁸ m/s

Required to find: The masses of the fragments.

Solution:

From the Conservation of Mass, since the total mass of the particle is constant,

----(1), where m₁ and m₂ are the masses of the fragments.

From the Conservation of Momentum,

Since the initial velocity of the particle is zero, the LHS of the above equation becomes zero.

[Cancelling 'c' on both sides and rearranging]

----(2)

Putting the value of equation (2) into (1),

Therefore the value of m₁,

Answer: The mass of the fragments are m_(0.976c) = 1.566414*10^-27 Kg and m_(-0.862c) = 1.773586*10^-27 Kg.

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genius_generous answered 1 year ago

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