The total energy of an electron in the nth stationary orbit of the hydrogen atom can be obtained by

An electron in a hydrogen atom (Bohr model) makes a transition from n = 2 state to n = 1 state. The frequency of the emitted photon is (take R = 1.0 × $$10^7$$​ $$\text{m}{^{-1}}$$​):

Rutherford scattering proved the:

Suppose that an alpha particle of 4.50 MeV approaches head-on a uranium nucleus (Z = 92). Assuming that the uranium nucleus remains at rest and the alpha particle momentarily comes to rest and reverses its direction at a distance much more than the radius of the uranium nucleus, the distance of its closest approach is close to:

Consider the mass of iron nucleus as 55.85 u and A = 56. Then the nuclear density is:

Consider two nuclei, A of mass number 27 and B of mass number 64. Considering them as liquid-drops, the ratio of their densities $$(\frac{d_A}{d_B})$$​ will be:

The ratio of the longest wavelength to the shortest wavelength ($$\frac{λ_L}{λ_S}$$​) in Brackett series of hydrogen spectrum is:

Rutherford scattering experiment is based on:

Suppose that an alpha particle of 3.20 MeV approaches head-on a lead nucleus (Z = 82). Assuming that the lead nucleus remains at rest and the alpha particle momentarily comes to rest and reverses its direction at a distance much more than the radius of the lead nucleus, the distance of its closest approach is:

The ratio of the longest wavelength to the shortest wavelength ($$\frac{λ_L}{λ_S}$$​ in Paschen series of hydrogen spectrum is:

Consider the solar system as a large atom. The quantum number (n) that characterises Earth's orbit (radius = 1.5 × $$10^{11}$$​ m) with Earth moving at an orbital speed of 3 × $$10^4$$​ m/s is (mass of Earth is 6 × $$10^{24}$$​ kg):