According to Bohr's theory,the electron in orbits has definite energy values. Then,according to the uncertainty principle,the lifetime of an excited state will be:

Using the Heisenberg uncertainty principle,arrange the following particles in the order of increasing lowest energy possible.
$(I)$ An electron in $H_{2}$ molecule
$(II)$ $A$ hydrogen atom in a $H_{2}$ molecule
$(III)$ $A$ proton in the carbon nucleus
$(IV)$ $A$ $H_{2}$ molecule within a nanotube

Explain the method of the Davisson and Germer experiment and its results.

The wave nature of electrons suggests that they will produce diffraction effects. Davisson and Germer experimentally proved this by diffracting electrons from a crystal. The law of diffraction from a crystal is obtained from the constructive interference of electron waves reflected from the planes of atoms in the crystal. Electrons accelerated by a potential $V$ are diffracted by a crystal. If $d = 1 \ \mathring{A}$ and $i = 30^\circ$,then the value of $V$ should be ........... $V$. $(h = 6.6 \times 10^{-34} \ J \cdot s, m_e = 9.1 \times 10^{-31} \ kg, e = 1.6 \times 10^{-19} \ C)$

The wave nature of electrons suggests that they will produce diffraction effects. Davisson and Germer experimentally proved this by diffracting electrons from a crystal. The law of diffraction from a crystal is obtained from the constructive interference of electron waves reflected from the planes of atoms in the crystal. When electrons are incident on the crystal plane at an angle $i$ with the normal to the plane,and the distance between the planes is $d$,which of the following equations can be used to calculate the de Broglie wavelength of the electrons if a sharp diffraction peak is obtained?

In the Davisson-Germer experiment,an electron beam of energy $75 \ eV$ falls normally on the surface of a crystal. If the maximum intensity is obtained at an angle of $45^o$ to the direction of the incident beam,then the inter-atomic distance in the lattice plane of the crystal will be .............. $\mathring{A}$