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?

Energy of an electron in an excited hydrogen atom is – 3.4 eV. Its angular momentum will be:
h = $6.626\times {10}^{-34} \mathrm{J}-\mathrm{s}$

(1) $1.11\times {10}^{-34} \mathrm{J} \sec$       

(2) $1.51\times {10}^{-31} \mathrm{J} \sec$

(3) $2.11\times {10}^{-34} \mathrm{J} \sec$       

(4) $3.72\times {10}^{-34 }\mathrm{J} \sec$

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) $1.215\times {10}^{-3} \mathrm{m}$

Energy of the electron in nth orbit of hydrogen atom is given by ${\mathrm{E}}_{\mathrm{n}}=-\frac{13.6}{{\mathrm{n}}^2}\mathrm{eV}$. The amount of energy needed to transfer electron from first orbit to third orbit is

(1) 13.6 eV             

(2) 3.4 eV

(3) 12.09 eV           

(4) 1.51 eV

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

An electron changes its position from orbit n = 4 to the orbit n = 2 of an atom. The wavelength of the emitted radiation’s is (R = Rydberg’s constant)

(1) $\frac{16}{\mathrm{R}}$             

(2) $\frac{16}{3\mathrm{R}}$

(3) $\frac{16}{5\mathrm{R}}$             

(4) $\frac{16}{7\mathrm{R}}$

What is the ratio of wavelength of radiations emitted when an electron in hydrogen atom jump from fourth orbit to second orbit and from third orbit to second orbit

(1) 27 : 25               

(2) 20 : 27

(3) 20 : 25               

(4) 25 : 27

The ground state energy of hydrogen atom is – 13.6 eV. What is the potential energy of the electron in this state

1. 0 eV                       

2. – 27.2 eV

3. 1 eV                       

4. 2 eV