If the kinetic energy of a particle is increased to $4$ times its initial value,how many times will the associated de Broglie wavelength become?

The wavelength associated with a particle of mass $9.109 \times 10^{-31} \ kg$ moving with a velocity of $1.20 \times 10^5 \ m/s$ is ....... meters.

If the radius of the first orbit of hydrogen atom is $a_0$, then de Broglie's wavelength of electron in $3^{rd}$ orbit is (in $\pi a_0$)

Calculate the wavelength of an electron if its mass is $9.1 \times 10^{-31} \, kg$,its velocity is $1/10$ of the speed of light,and the value of Planck's constant $h$ is $6.626 \times 10^{-34} \, J \cdot s$.

According to de Broglie,matter should exhibit dual behaviour,that is both particle and wave-like properties. However,a cricket ball of mass $100 \ g$ does not move like a wave when it is thrown by a bowler at a speed of $100 \ km/h$. Calculate the wavelength of the ball and explain why it does not show wave nature.

Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.