Calculate the $\lambda$ associated with an electron moving with the velocity of light.

The atomic masses of $He$ and $Ne$ are $4$ and $20 \ amu$,respectively. The value of the de Broglie wavelength of $He$ gas at $-73^{\circ} C$ is $M$ times that of the de Broglie wavelength of $Ne$ at $727^{\circ} C$. $M$ is

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

For the quantization of the Bohr orbit,its circumference will be equal to .......

If the de Broglie wavelength of the electron in the $n^{th}$ Bohr orbit in a hydrogenic atom is equal to $1.5 \, \pi \, a_0$ ($a_0$ is Bohr radius),then the value of $n/Z$ is:

Dual behavior of matter proposed by de Broglie led to the discovery of electron microscope, often used for the highly magnified images of biological molecules and other types of material. If the velocity of the electron in this microscope is $1.6 \times 10^{6} \,ms^{-1}$, calculate the de Broglie wavelength associated with this electron.