A hydrogen atom in its ground state absorbs 10.2 eV of energy. The orbital angular momentum is increased by-  (Given Planck constant h = $6.6\times {10}^{-34}$ J-sec)

1. $1.05\times {10}^{-34}$ J-sec                 2. $3.16\times {10}^{-34}$ J-sec
3. $2.11\times {10}^{-34}$ J-sec                 4. $4.22\times {10}^{-34}$J-sec

Hydrogen (H), deuterium (D), singly ionized helium and doubly ionized lithium all have one electron around the nucleus. Consider n =2 to n = 1 transition. The wavelengths of emitted radiations are ${\mathrm{\lambda }}_1,{\mathrm{\lambda }}_2,{\mathrm{\lambda }}_3$ and ${\mathrm{\lambda }}_4$ respectively. Then approximately 
(a) ${\mathrm{\lambda }}_1={\mathrm{\lambda }}_2=4{\mathrm{\lambda }}_3=9{\mathrm{\lambda }}_4$                             (b) $4{\mathrm{\lambda }}_1=2{\mathrm{\lambda }}_2=2{\mathrm{\lambda }}_3={\mathrm{\lambda }}_4$
(c) ${\mathrm{\lambda }}_1=2{\mathrm{\lambda }}_2=2\sqrt{2}{\mathrm{\lambda }}_3=3\sqrt{2}{\mathrm{\lambda }}_4$                 (d) ${\mathrm{\lambda }}_1={\mathrm{\lambda }}_2=2{\mathrm{\lambda }}_3=3\sqrt{2}{\mathrm{\lambda }}_4$

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

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 neutron with velocity V strikes a stationary deuterium atom. Its kinetic energy changes by a factor of 
(1) $\frac{15}{16}$             

(2) $\frac{1}{2}$

(3) $\frac{2}{1}$               

(4) None of these

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 transition from the state n = 4 to n = 3 in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition:

(1) 2$\to$1                 

(2) 3$\to$2

(3) 4$\to$2

(4) 5$\to$4

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