For which of the following does the mathematical expression $\lambda = \frac{h}{p}$ stand?

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

If $v_0$ is the threshold frequency of a metal $X$,the correct relation between de Broglie wavelength $(\lambda)$ associated with the photoelectron and the frequency $(v)$ of the incident radiation is:

What is the characteristic of an electron microscope? On which principle is it based?

When light of wavelength $248 \, nm$ falls on a metal of threshold energy $3.0 \, eV$,the de-Broglie wavelength of emitted electrons is ............. $\mathring{A}$ (Round off to the Nearest Integer). [Use : $\sqrt{3}=1.73, h =6.63 \times 10^{-34} \, Js, m_e =9.1 \times 10^{-31} \, kg, c =3.0 \times 10^{8} \, ms^{-1}, 1 \, eV =1.6 \times 10^{-19} \, J$]

The mass of an electron is $9.1 \times 10^{-31} \ kg$. If its $K.E.$ is $3.0 \times 10^{-25} \ J$,calculate its wavelength.