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:

When a hydrogen atom is raised from the ground state to an excited state:

In Bohr's model if the atomic radius of the first orbit is r₀, then what will be the radius of the third orbit?
1. $\frac{{\mathrm{r}}_0}{9}$              

2. ${\mathrm{r}}_0$
3. $9{\mathrm{r}}_0$               

4. $3{\mathrm{r}}_0$

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?

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

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

Given that the value of the Rydberg constant is \(10^{7}~\text{m}^{-1}\), what will be the wave number of the last line of the Balmer series in the hydrogen spectrum?
1. \(0.5 \times 10^{7}~\text{m}^{-1}\)
2. \(0.25 \times 10^{7} ~\text{m}^{-1}\)
3. \(2.5 \times 10^{7}~\text{m}^{-1}\)
4. \(0.025 \times 10^{4} ~\text{m}^{-1}\)

The ratio of the longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is:

If an alpha nucleus of energy $\frac{1}{2}m{v}^2$ bombards a heavy nuclear target of charge Ze, then the distance of closest approach for the alpha nucleus will be proportional to: