Question

What is the de Broglie wavelength (in cm) of a 160g cricket ball travelling at140 Km hr⁻¹.

Answer 1

The De-Broglie Hypothesis states that all matter particles behave like waves too.

This concept extends the Wave-Particle Duality to all matter particles. The  mathematical formulation is:

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

Here,
$\lambda$ = Wavelength of matter particle
$h$ = Planck's Constant = $6.626 \times 10^{-34} \, \, J \, s$
$p$ = Momentum of particle
$m$ = Mass of particle
$v$ = Velocity of particle

Here, we are given a cricket ball which is travelling at some velocity. Our data is:


$m = 160 \, \, g = 0.16 \, \, kg \\ \\ v = 140 \, \, km/h = 140 \times \frac{5}{18} \, \, m/s = \frac{350}{9} \, \, m/s$


Now, we can find the wavelength of the cricket ball.



$\lambda = \frac{h}{mv} \\ \\ \\ \implies \lambda = \frac{6.626 \times 10^{-34}}{0.16 \times \frac{350}{9}} \\ \\ \\ \implies \lambda = \frac{6.626\times 9\times 10^{-34}}{0.16\times 350} \\ \\ \\ \implies \boxed{\lambda \approx 1.065 \times 10^{-34} \, \, m}$


Thus, the wavelength of the cricket ball is $1.065\times 10^{-34}$ metres.



Hope it helps
Purva
Brainly Community