91Ó°ÊÓ

If the radius of an orbit is \(\mathrm{r}\) and the velocity of the electron in it is \(\mathrm{v}\), then the frequency of electron in the orbit will be - (a) \(2 \pi \mathrm{rv}\) (b) \(\frac{2 \pi}{\mathrm{vr}}\) \(\begin{array}{ll}\text { (c) } \frac{\mathrm{vr}}{2 \pi} & \text { (d) } \frac{\mathrm{v}}{2 \pi \mathrm{r}}\end{array}\)

In Bohr's model of hydrogen atom- (a) The radius of \(\mathrm{n}^{\text {th }}\) orbit is proportional to \(\mathrm{n}^{2}\) (b) The total energy of electron in \(\mathrm{n}^{\text {th }}\) orbit is proportional to \(\mathrm{n}\). (c) The angular momentum of the electron in an orbit is an integral multiple of \(\mathrm{h} / 2 \pi\) (d) The magnitude of the potential energy of an electron in any orbit is greater than its kinetic energy.

According to the Bohr's theory of a hydrogen atom, for the electron in the \(\mathrm{n}^{\text {th }}\) permissible orbit. (a) Linear momentum \(\propto \frac{1}{\mathrm{n}}\) (b) radius of orbit \(\propto \mathrm{n}\) (c) Kinetic energy \(\propto \frac{1}{\mathrm{n}^{2}}\) (d) angular momentum \(\propto \mathbf{n}\)

The energy levels of a hypothetical one electron atom are given by $$ \mathrm{E}_{\mathrm{n}}=-\frac{18.0}{\mathrm{n}^{2}} \mathrm{eV}, \text { where } \mathrm{n}=1,2,3 \ldots . $$ Compute the four lowest energy levels and construct the energy level diagram. (a) \(-18.0 \mathrm{eV},-4.5 \mathrm{eV},-2.0 \mathrm{eV},-1.125 \mathrm{eV}\) (b) \(-4.5 \mathrm{eV},-19 \mathrm{eV},-1.125 \mathrm{eV}, 2 \mathrm{eV}\) (c) \(2 \mathrm{eV},-4.6 \mathrm{eV},-1.125 \mathrm{eV}, 18 \mathrm{eV}\) (d) \(-1.125 \mathrm{eV}, 18 \mathrm{eV}, 2 \mathrm{eV},-4.5 \mathrm{eV}\)