To find the mass of the particle, we can use the kinetic energy formula provided:

$\text{Kinetic Energy (KE)} = \frac{1}{2} \times \text{mass} \times \text{velocity}^2$

Given values:

• Kinetic Energy ($KE$) = $8.73 \times 10^{-17} \, \text{J}$
• Velocity ($v$) = $5.00 \times 10^6 \, \text{m/s}$

Step-by-Step Solution:

1. Rearrange the kinetic energy formula to solve for mass $m$: $m = \frac{2 \times KE}{v^2}$

2. Substitute the given values: $m = \frac{2 \times (8.73 \times 10^{-17})}{(5.00 \times 10^6)^2}$

3. Calculate $(5.00 \times 10^6)^2$: $(5.00 \times 10^6)^2 = 2.5 \times 10^{13}$

4. Substitute and compute $m$: $m = \frac{2 \times 8.73 \times 10^{-17}}{2.5 \times 10^{13}}$

5. Simplify the expression: $m = \frac{1.746 \times 10^{-16}}{2.5 \times 10^{13}} = 6.984 \times 10^{-30}$

6. Round to three significant figures as required: $m = 6.98 \times 10^{-30}$

Answer:

The mass of the particle, to three significant figures and in the required format, is:

$6.98\text{E-30}$

Would you like further details or have any questions?

Here are five related questions for further exploration:

1. How would the mass change if the velocity were doubled?
2. What is the relationship between kinetic energy and mass if the velocity is constant?
3. How does the kinetic energy formula apply to objects at relativistic speeds?
4. If the kinetic energy of a particle changes, how does its velocity change assuming constant mass?
5. What units are typically used for each variable in the kinetic energy equation?

Tip: When working with scientific notation, keep track of powers of ten carefully to avoid calculation errors.