The kinetic energy of a subatomic particle is `5.85 xx 10^(-25) J`. Calculate the frequency of the particle wave.

Explanation

To calculate the frequency of a particle wave given its kinetic energy, we can use the relationship between kinetic energy (KE) and frequency (f) derived from the de Broglie hypothesis. The kinetic energy of a particle is related to its frequency by the equation:

\[ KE = h \cdot f \]

where:
- \( KE \) is the kinetic energy,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)),
- \( f \) is the frequency.

### Step-by-step solution:

1. **Identify the given values**:
- Kinetic Energy (KE) = \( 5.85 \times 10^{-25} \, \text{J} \)
- Planck's constant (h) = \( 6.626 \times 10^{-34} \, \text{J s} \)

2. **Rearrange the equation to solve for frequency (f)**:
\[ f = \frac{KE}{h} \]

3. **Substitute the values into the equation**:
\[ f = \frac{5.85 \times 10^{-25} \, \text{J}}{6.626 \times 10^{-34} \, \text{J s}} \]

4. **Calculate the frequency**:
\[ f = \frac{5.85 \times 10^{-25}}{6.626 \times 10^{-34}} \approx 8.82 \times 10^{8} \, \text{Hz} \]

### Final Answer:
The frequency of the particle wave is approximately \( 8.82 \times 10^{8} \, \text{Hz} \).