The wavelength of the energy emitted when electrons come from the fourth orbit to the second orbit in hydrogen is \(20.397~\text{cm}\). The wavelength of energy for the same transition in \(\mathrm{He^{+}}\) is:
1. \(5.099~\text{cm}\)
2. \(20.497~\text{cm}\)
3. \(40.994~\text{cm}\)
4. \(81.988~\text{cm}\)

Which of the following statements are true regarding Bohr's model of hydrogen atom?

(I) Orbiting speed of electron decreases as it shifts to discrete orbits away from the nucleus

(II) Radii of allowed orbits of electron are proportional to  principal quantum number

(III) Frequency with which electrons orbits around the nucleus in discrete orbits is inversely proportional to the cube of principal quantum number

(IV) Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbits
Select correct answer using the codes given below
Codes :
(1) I and III                 

(2) II and IV

(3) I, II and III           

(4) II, III and IV

Radius of the first orbit of the electron in a hydrogen atom is 0.53 Å. So, the radius of the third orbit will be

(1) 2.12 Å             

(2) 4.77 Å

(3) 1.06 Å             

(4) 1.59 Å

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