Step 1: Understanding the Question:
The question asks for the wavelength associated with matter (de Broglie wavelength) when that matter has no velocity.
Step 2: Key Formula or Approach:
The de Broglie wavelength \(\lambda\) is given by:
\[ \lambda = \frac{h}{p} = \frac{h}{mv} \]
where \(h\) is Planck's constant, \(m\) is mass, and \(v\) is velocity.
Step 3: Detailed Explanation:
For a particle at rest, the velocity \(v = 0\).
Substituting this into the momentum formula:
\[ p = m \times 0 = 0 \]
Now, substituting the momentum into the wavelength formula:
\[ \lambda = \frac{h}{0} \]
In mathematical limits, a finite value divided by zero tends toward infinity (\(\infty\)).
Step 4: Final Answer:
The wavelength of a particle at rest is infinite.