The frequency of the series limit of the Balmer series of hydrogen atoms in terms of Rydberg constant R and velocity of light C is:

1. $\frac{RC}{4}$

2. RC

3. $\frac{4}{RC}$

4. 4RC

The energy of an electron in an excited hydrogen atom is -3.4 eV.  Its angular momentum will be:
(h = 6.626 $\times$ 10^-34 J-s)

1. 1.11 $\times$ 10³⁴ J s 

2. 1.51 $\times$10^-31 J s

3. 2.11 $\times$ 10^-34 J s

4. 3.72 $\times$ 10^-34 J s

The radius of a hydrogen atom in its ground state is 5.3×10^-11 m. After collision with an electron, it is found to have a radius of 21.2 ×10^-11 m. What is the principal quantum number n of the final state of the atom?

1. n = 4 

2. n = 2 

3. n = 16 

4. n = 3

A hydrogen atom is in an excited state of principal quantum number (n). It emits a photon of wavelength ($\lambda$) when it returns to the ground state. The value of n is:

1. $\sqrt{\frac{\lambda R}{\lambda R-1}}$ 

2. $\sqrt{\frac{(\lambda R-1)}{\lambda R}}$

3. $\sqrt{\lambda (R-1)}$ 

4. None of these

Hydrogen ₁H¹, Deuterium ₁H², singly ionised helium (₂He⁴)⁺, and doubly ionised lithium (₃Li⁶)⁺⁺ all have one electron around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wavelengths of emitted radiations are λ₁ ,λ₂ ,λ₃ and  λ₄ respectively, then approximately which one of the following is correct?

If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength $\lambda$. What will be the corresponding wavelength of the photon when it jumps from the 4^th orbit to the 3rd orbit?

1. $\frac{16}{25}\lambda$               

2. $\frac{9}{16}\lambda$

3. $\frac{20}{7}\lambda$               

4. $\frac{20}{13}\lambda$

Considering the 3^rd orbit of He+ (Helium ion), using the non-relativistic approach, the speed of the electron in this orbit will be: (Given: Z=2, K=9x10⁹, and Planck's constant, h=6.6x10^-34 J-s)
1. 2.92x10⁸ m/s
2. 1.46x${10}^6$ m/s
3. 0.73x10⁸ m/s
4. 3.0x10⁸ m/s

In a Rutherford scattering experiment when a projectile of charge $Z_1$ and mass $M_1$ approaches a target nucleus of charge $Z_2$ and mass $M_2,$ the distance of closest approach is $r_0$. What is the energy of the projectile?

In the n^th orbit, the energy of an electron is \(\mathrm{E}_{\mathrm{n}}=-\frac{13.6}{\mathrm{n}^2} \mathrm{~eV}\) 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 eV

2. 12.1 eV 

3. 13.6 eV

4. 3.4 eV 

A beam of fast-moving alpha particles were directed towards a thin film of gold. The parts A', B', and C' of the transmitted and reflected beams corresponding to the incident parts A, B and C of the beam, are shown in the adjoining diagram. The number of alpha particles in: