Question

determine the velocity of a neutron that has (e_{k}=8.03\times 10^{-15}\text{ j}). be sure your answer has the correct number of significant figures. note: the mass of a neutron is (1.675\times 10^{-24}\text{ g}).

Explanation:

Step1: Recall the kinetic - energy formula

The kinetic - energy formula is $E_{k}=\frac{1}{2}mv^{2}$, where $E_{k}$ is the kinetic energy, $m$ is the mass, and $v$ is the velocity. We need to solve for $v$, so we can re - arrange the formula to $v = \sqrt{\frac{2E_{k}}{m}}$.

Step2: Convert the mass unit

The mass of the neutron $m = 1.675\times10^{-24}\text{ g}$. We need to convert it to kg. Since $1\text{ g}=10^{-3}\text{ kg}$, then $m = 1.675\times10^{-27}\text{ kg}$. The kinetic energy $E_{k}=8.03\times10^{-15}\text{ J}$.

Step3: Substitute values into the formula

Substitute $E_{k}=8.03\times10^{-15}\text{ J}$ and $m = 1.675\times10^{-27}\text{ kg}$ into $v=\sqrt{\frac{2E_{k}}{m}}$.
\[

$$\begin{align*} v&=\sqrt{\frac{2\times8.03\times10^{-15}}{1.675\times10^{-27}}}\\ &=\sqrt{\frac{16.06\times10^{-15}}{1.675\times10^{-27}}}\\ &=\sqrt{9.588\times10^{12}}\\ &\approx 3.10\times 10^{6}\text{ m/s} \end{align*}$$

\]

Answer:

$3.10\times 10^{6}\text{ m/s}$