The energy of separation of an electron in a Hydrogen-like atom in an excited state is $3.4 \ eV$. The de-Broglie wavelength (in $\mathring{A}$) associated with the electron is (Given: radius of the first orbit of $H$ atom is $0.53 \ \mathring{A}$)

The de-Broglie wavelength associated with a particle of mass $10^{-6} \ kg$ with a velocity of $10 \ ms^{-1}$ is $:-$

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.

If the velocity of the electron in Bohr's first orbit is $2.19 \times 10^{6} \, m s^{-1}$, calculate the de Broglie wavelength associated with it.

$A$ $0.66 \ kg$ ball is moving with a speed of $100 \ m/s$. The associated wavelength will be $(h = 6.6 \times 10^{-34} \ J \ s)$.

Two base balls (masses: $m_1 = 100 \ g$ and $m_2 = 50 \ g$) are thrown. Both of them move with uniform velocity, but the velocity of $m_2$ is $1.5$ times that of $m_1$. The ratio of de Broglie wavelengths $\lambda(m_1) : \lambda(m_2)$ is given by