For the Bohr's first orbit of circumference $2\mathrm{\pi r}$, the de-Broglie wavelength of revolving electron will be

(a) $2\mathrm{\pi r}$                       (b) $\mathrm{\pi r}$
(c) $\frac{1}{2\mathrm{\pi r}}$                      (d) $\frac{1}{4\mathrm{\pi r}}$

According to de-Broglie, the de-Broglie wavelength for electron in an orbit of hydrogen atom is ${10}^{-10}$ m. The principle quantum number for this electron is $\left(r=5.13\times {10}^{-11}m\right)$
(a) 1           (b) 2
(c) 3           (d) 4

The energy of a photon of light with wavelength 5000 Å is approximately 2.5 eV. This way the energy of an X-ray photon with wavelength 1Å would be 
(1) 2.5/5000 eV             

(2) $2.5/{\left(5000\right)}^2 \mathrm{eV}$

(3) $2.5\times 5000 \mathrm{eV}$           

(4)  $2.5\times {\left(5000\right)}^2 \mathrm{eV}$

The graph that correctly represents the relation of frequency v of a particular characteristic X-ray with the atomic number Z of the material is

If in nature there may not be an element for which the principal quantum number n > 4, then the total possible number of elements will be

(1) 60                   

(2) 32

(3) 4                     

(4) 64

In the \(n^{th}\) orbit, the energy of an electron is \(E_{n}=-\frac{13.6}{n^2} ~\text{eV}\) for the hydrogen atom. What will be the energy required to take the electron from the first orbit to the second orbit?
1. \(10.2~\text{eV}\)
2. \(12.1~\text{eV}\)
3. \(13.6~\text{eV}\)
4. \(3.4~\text{eV}\)

The Lyman series of hydrogen spectrum lies in the region

(1) Infrared               

(2) Visible

(3) Ultraviolet             

(4) X- rays

Which one of the series of hydrogen spectrum is in the visible region 

1. Lyman series             

2. Balmer series

3. Paschen series           

4. Bracket series

The Rutherford $\mathrm{\alpha }$-particle experiment shows that most of the $\mathrm{\alpha }$-particles pass through almost unscattered while some are scattered through large angles. What information does it give about the structure of the atom 

(1) Atom is hollow

(2) The whole mass of the atom is concentrated in a small centre called nucleus

(3) Nucleus is positively charged

(4) All the above

Which of the following is true 

(1) Lyman series is a continuous spectrum

(2) Paschen series is a line spectrum in the infrared

(3) Balmer series is a line spectrum in the ultraviolet

(4) The spectral series formula can be derived from the Rutherford model of the hydrogen atom