JEE Advance - Chemistry (2004 - No. 7)

To find the wavelength of a ball moving with a certain velocity, we use the de Broglie wavelength formula:

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

Where:

• $\lambda$ is the wavelength,


• $h$ is Planck's constant, which is approximately $6.626 \times 10^{-34} \, \text{Js}$ (joule-second),


• $p$ is the momentum of the object, calculated as the product of its mass ($m$) and velocity ($v$).

Given that the mass ($m$) of the ball is 100 g (which should be converted to kilograms to be consistent with the SI units), so $m = 0.1 \, \text{kg}$, and the velocity ($v$) of the ball is $100 \, \text{m/s}$, we can calculate the momentum ($p$) as:

$p = m \cdot v = 0.1 \, \text{kg} \cdot 100 \, \text{m/s} = 10 \, \text{kg} \cdot \text{m/s}$

Now, substituting the values of $h$ and $p$ into the de Broglie wavelength equation:

$\lambda = \frac{6.626 \times 10^{-34} \, \text{Js}}{10 \, \text{kg} \cdot \text{m/s}}$

$\lambda = 6.626 \times 10^{-35} \, \text{m}$

So, the wavelength of the ball moving at a velocity of $100 \, \text{m/s}$ is $6.626 \times 10^{-35} \, \text{m}$, which is an extremely small wavelength, demonstrating the particle nature of macroscopic objects becomes significant only at the quantum scale.