The electric potential between a proton and an electron is given by $\mathrm{V}={\mathrm{V}}_0\ln \frac{\mathrm{r}}{{\mathrm{r}}_0}$ where ${\mathrm{r}}_0$ is a constant. Assuming Bohr’s model to be applicable, the variation of ${\mathrm{r}}_{\mathrm{n}}$ with n, n being the principal quantum number, is:

1. ${\mathrm{r}}_{\mathrm{n}}\propto \mathrm{n}$           

2. ${\mathrm{r}}_{\mathrm{n}}\propto 1/\mathrm{n}$

3. ${\mathrm{r}}_{\mathrm{n}}\propto {\mathrm{n}}^2$           

4. ${\mathrm{r}}_{\mathrm{n}}\propto 1/{\mathrm{n}}^2$

If the atom ${}_{100}{}^{257}\mathrm{Fm}$ follows the Bohr model and the radius of ${}_{100}{}^{257}\mathrm{Fm}$ is n times the Bohr radius, then the value of n is:

(1) 100               
(2) 200
(3) 4                   
(4) $\frac{1}{4}$

Consider a hydrogen like atom whose energy in nth exicited state is given by ${\mathrm{E}}_{\mathrm{n}}=-\frac{13.6 {\mathrm{Z}}^2}{{\mathrm{n}}^2}$ when this excited atom makes a transition from excited state to ground state, most energetic photons have energy ${\mathrm{E}}_{\max }$ = 52.224 eV and least energetic photons have energy ${\mathrm{E}}_{\min }$ = 1.224 eV. The atomic number of atom is
(a) 2                 (b) 5
(c) 4                 (d) None of these

When a hydrogen atom is excited from ground state to first excited state then the incorrect option is– 

1. its kinetic energy increases by $10.2 \mathrm{eV}$ 

2. its kinetic energy decreases by $10.2 \mathrm{eV}$ 

3. its potential energy increases by $20.4 \mathrm{eV}$ 

4. its angular momentum increases by $1.05 \times {10}^{–34} \mathrm{J}$-s

In the Bohr model of the hydrogen atom, let R, v and E represent the radius of the orbit, the speed of electron and the total energy of the electron respectively. Which of the following quantity is proportional to the quantum number n ?

(1) R/E               

(2) E/v

(3) RE               

(4) vR

Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength $\mathrm{\lambda }$ (given in terms of the Rydberg constant R for the hydrogen atom) equal to

(1) 9/(5R)                 
(2) 36/(5R)
(3) 18/(5R)               
(4) 4/R

The ionisation potential of H-atom is  13.6 V. When it is excited from ground state by monochromatic radiations of $970.6 \stackrel{0}{\mathrm{A}}$, the number of emission lines will be (according to Bohr’s theory) 
(1) 10           

(2) 8

(3) 6             

(4) 4

A double charged lithium atom is equivalent to hydrogen whose atomic number is 3. The wavelength of required radiation for exciting electron from first to third Bohr orbit in ${\mathrm{Li}}^{++}$ will be (Ionisation energy of hydrogen atom is 13.6eV) 
(a) 182.51 Å                 (b) 177.17 Å
(c) 142.25 Å                 (d) 113.74 Å

In a hypothetical Bohr hydrogen, the mass of the electron is doubled. What will be the energy E₀ and the radius r₀ of the first orbit?
(${\mathrm{a}}_0$ is the Bohr radius) 

The ratio of the speed of the electrons in the ground state of hydrogen to the speed of light in vacuum is

1. 1/2                2. 2/137
3. 1/137            4. 1/237