Questions: A nucleus moving at a speed of 2.5 × 10^8 m / s crashes into a device that measures its kinetic energy to be 1.24 × 10^-9 J. What is the mass of this nucleus?

A nucleus moving at a speed of 2.5 × 10^8 m / s crashes into a device that measures its kinetic energy to be 1.24 × 10^-9 J. What is the mass of this nucleus?
Transcript text: A nucleus moving at a speed of $2.5 \times 10^{8} \mathrm{~m} / \mathrm{s}$ crashes into a device that measures its kinetic energy to be $1.24 \times 10^{-9} \mathrm{~J}$. What is the mass of this nucleus?
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Solution

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Solution Steps

Step 1: Identify the Known Variables

We are given the speed of the nucleus, \( v = 2.5 \times 10^8 \, \text{m/s} \), and its kinetic energy, \( KE = 1.24 \times 10^{-9} \, \text{J} \).

Step 2: Use the Kinetic Energy Formula

The formula for kinetic energy is: \[ KE = \frac{1}{2} m v^2 \] where \( m \) is the mass of the nucleus.

Step 3: Solve for Mass

Rearrange the kinetic energy formula to solve for mass \( m \): \[ m = \frac{2 \times KE}{v^2} \]

Step 4: Substitute the Known Values

Substitute the given values into the equation: \[ m = \frac{2 \times 1.24 \times 10^{-9} \, \text{J}}{(2.5 \times 10^8 \, \text{m/s})^2} \]

Step 5: Calculate the Mass

Calculate the mass: \[ m = \frac{2.48 \times 10^{-9}}{6.25 \times 10^{16}} \] \[ m = 3.968 \times 10^{-26} \, \text{kg} \]

Final Answer

The mass of the nucleus is \(\boxed{3.968 \times 10^{-26} \, \text{kg}}\).

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