The first line in the Lyman series has wavelength $\mathrm{\lambda }$. The wavelength of the first line in Balmer series is

(1) $\frac{2}{9}\mathrm{\lambda }$             

(2) $\frac{9}{2}\mathrm{\lambda }$
(3) $\frac{5}{27}\mathrm{\lambda }$           

(4) $\frac{27}{5}\mathrm{\lambda }$

In the following transitions, which one has higher frequency

(1) 3 – 2             

(2) 4 – 3

(3) 4 – 2             

(4) 3 – 1

The diagram depicts the paths of four \(\alpha\)-particles with identical energies being scattered simultaneously by the nucleus of an atom. Which of these paths are/is not physically possible?
                
1. \((3)\) & \((4)\)
2.  \((2)\) & \((3)\)
3.  \((1)\) & \((4)\)
4. \((4)\) only

An electron jumps from 5th orbit to 4th orbit of hydrogen atom. Taking the Rydberg constant as  ${10}^7$ per metre. What will be the frequency of radiation emitted

(1) $6.75\times {10}^{12} \mathrm{Hz}$             

(2) $6.75\times {10}^{14} \mathrm{Hz}$

(3) $6.75\times {10}^{13} \mathrm{Hz}$             

(4) None of these

Four lowest energy levels of H-atom are shown in the figure. The number of possible emission lines would be

(1) 3             

(2) 4

(3) 5             

(4) 6

The wavelength of light emitted when an electron jumps from second orbit to first orbits in a hydrogen atom is 
(a) $1.215\times {10}^{-7} \mathrm{m}$         (b) $1.215\times {10}^{-5} \mathrm{m}$
(c) $1.215\times {10}^{-4} \mathrm{m}$          (d) $1.215\times {10}^{-3} \mathrm{m}$

The de-Broglie wavelength of an electron in the first Bohr orbit is 

(1) Equal to one fourth the circumference of the first orbit

(2) Equal to half the circumference of the first orbit

(3) Equal to twice the circumference of the first orbit

(4) Equal to the circumference of the first orbit

The frequency of 1st line of Balmer series in ${\mathrm{H}}_2$ atom is ${\mathrm{v}}_0$. The frequency of line emitted by singly ionised He atom is

(1) 2${\mathrm{v}}_0$          

(2) 4${\mathrm{v}}_0$

(3) ${\mathrm{v}}_0$/2         

(4) ${\mathrm{v}}_0$/4

When the electron in the hydrogen atom jumps from 2nd orbit to 1st orbit, the wavelength of radiation emitted is $\mathrm{\lambda }$. When the electrons jump from 3rd orbit to 1st orbit, the wavelength of emitted radiation would be

 
(1) $\frac{27}{32}\mathrm{\lambda }$             

(2) $\frac{32}{27}\mathrm{\lambda }$

(3) $\frac{2}{3}\mathrm{\lambda }$               

(4) $\frac{3}{2}\mathrm{\lambda }$

Which of the following transition will have shortest emission wavelength ?

(1) n = 2 to n =1           

(2) n = 1 to n = 2 

(3) n = 2 to n = 5         

(4) n = 5 to n = 2