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

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

Taking Rydberg’s constant ${\mathrm{R}}_{\mathrm{H}}=1.097\times {10}^7 \mathrm{m}$ first and second wavelength of Balmer series in hydrogen spectrum is

(a) 2000 Å, 3000 Å                  (b) 1575 Å, 2960 Å
(c) 6529 Å, 4280 Å                  (d) 6552 Å, 4863 Å

The energy of the highest energy photon of Balmer series of hydrogen spectrum is close to
(1) 13.6 eV             

(2) 3.4 eV
(3) 1.5 eV               

(4) 0.85 eV

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

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 
(a) 2$\to$1                  (b) 3$\to$2
(c) 4$\to$2                  (d) 5$\to$4

The hydrogen atom in the ground state is excited by monochromatic radiation of λ = 975 Å. The number of spectral lines in the resulting spectrum emitted will be :

1. 3

2. 2

3. 6

4. 10

X-ray is produced in a Coolidge tube at a given accelerating voltage. The wavelength of continuous X-rays has values from :

1.  Zero

2.  ${\lambda }_{min}\text{ to infinity and }{\lambda }_{min}>0$

3.  ${\lambda }_{min}\text{ to }{\lambda }_{max}\text{ and }0<{\lambda }_{min}<{\lambda }_{max}<\mathrm{\infty }$

4.  $\mathrm{Zero} \mathrm{to} {\mathrm{\lambda }}_{max}\text{ and }{\mathrm{\lambda }}_{max}<\mathrm{\infty }$

In Bohr model of hydrogen atom, the ratio of periods of revolution of an electron in \(n=2\) and \(n=1\) orbits is:
1. \(2:1\)             
2. \(4:1\)
3. \(8:1\)             
4. \(16:1\)

In Bohr's model, the atomic radius of the first orbit is ${\mathrm{r}}_0$, then the radius of the third orbit is
(1) $\frac{{\mathrm{r}}_0}{9}$              

(2) ${\mathrm{r}}_0$
(3) $9{\mathrm{r}}_0$               

(4) $3{\mathrm{r}}_0$