Answer:
Wavelength of the ball is [tex]\lambda=1.05\times 10^{-34}\ m[/tex]
Explanation:
It is given that,
Mass of the ball, m = 0.2 kg
It strikes the Earth after being dropped from a building of 50 m tall, h = 50 m
In this time, the potential energy is converted to kinetic energy. On applying the conservation of energy as :
[tex]\dfrac{1}{2}mv^2=mgh[/tex]
[tex]v=\sqrt{2gh}[/tex].............(1)
The De-broglie wavelength of the ball is given by :
[tex]\lambda=\dfrac{h}{mv}[/tex]
[tex]\lambda=\dfrac{h}{m\sqrt{2gh}}[/tex]
[tex]\lambda=\dfrac{6.63\times 10^{-34}\ J-s}{0.2\ kg\times \sqrt{2\times 9.8\ m/s^2\times 50\ m}}[/tex]
[tex]\lambda=1.05\times 10^{-34}\ m[/tex]
Hence, this is the required solution.
