The wavelength of a ball of mass 100 g moving with a velocity of $10~ms^{-1}$ is:

Question

Accepted Answer

To determine the wavelength of a ball of mass 100 g moving with a velocity of $10~\text{ms}^{-1}$, we use the de Broglie wavelength formula:

$$
\lambda = \frac{h}{mv}
$$

where:
- $\lambda$ is the wavelength,
- $h$ is Planck's constant ($6.626 \times 10^{-34} \text{Js}$),
- $m$ is the mass of the object in kilograms,
- $v$ is the velocity of the object in meters per second.

First, convert the mass from grams to kilograms:

$$
m = 100 \, \text{g} = 0.1 \, \text{kg}
$$

Now, substitute the values into the de Broglie wavelength formula:

$$
\lambda = \frac{6.626 \times 10^{-34} \text{Js}}{0.1 \, \text{kg} \times 10 \, \text{ms}^{-1}}
$$

$$
\lambda = \frac{6.626 \times 10^{-34}}{1}
$$

$$
\lambda = 6.626 \times 10^{-34} \, \text{m}
$$

This calculation shows that the wavelength of the ball is approximately $6.6 \times 10^{-34} \, \text{m}$, which corresponds to Option 1.

**Explanation for why Option 1 is correct:**
- The calculation using the de Broglie wavelength formula directly results in a wavelength of $6.6 \times 10^{-34} \, \text{m}$, which matches Option 1. This confirms that Option 1 is the correct answer.

**Explanation for why the other options are incorrect:**
- **Option 2: $6.6 \times 10^{-35} \, \text{m}$**: This option is incorrect because it suggests a wavelength that is ten times smaller than the calculated value. The calculation clearly shows that the wavelength is $6.6 \times 10^{-34} \, \text{m}$, not $6.6 \times 10^{-35} \, \text{m}$.
- **Option 3: $6.6 \times 10^{-36} \, \text{m}$**: This option is incorrect because it suggests a wavelength that is one hundred times smaller than the calculated value. The correct calculation yields $6.6 \times 10^{-34} \, \text{m}$.
- **Option 4: $6.6 \times 10^{-37} \, \text{m}$**: This option is incorrect because it suggests a wavelength that is one thousand times smaller than the calculated value. The correct wavelength is $6.6 \times 10^{-34} \, \text{m}$.

In conclusion, the correct answer is Option 1, $6.6 \times 10^{-34} \, \text{m}$, based on the accurate application of the de Broglie wavelength formula.