In a Rutherford scattering experiment when a projectile of charge Z₁ and mass M₁ approaches a target nucleus of charge Z₂ and mass M₂ the distance of the closest approach is r₀. What is the energy of the projectile?

The Bohr model for the spectra of a H-atom: (a) will not apply to hydrogen in the molecular form. (b) will not be applicable as it is for a He-atom. (c) is valid only at room temperature. (d) predicts continuous as well as discrete spectral lines. Choose the correct option:

Let En = -(me^4)/(8ε_0^2 n^2 h^2) be the energy of the nth level of H-atom. If all the H-atoms are in the ground state and radiation of frequency (E2 - E1)/h falls on it, then: (a) it will not be absorbed at all. (b) some of the atoms will move to the first excited state. (c) all atoms will be excited to the n=2 state. (d) no atoms will make a transition to the n=3 state. Choose the correct option:

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly ionized helium atom is:

Match List-I (Spectral Series) with List-II (corresponding wave number expressions). List-I (Series) A. Balmer series B. Lyman series C. Brackett series D. Pfund series List-II (Wave number in cm⁻¹) I. R(1/1² - 1/n²) II. R(1/4² - 1/n²) III. R(1/5² - 1/n²) IV. R(1/2² - 1/n²) Choose the correct answer from the options given below:

In the Bohr's model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If a₀ is the radius of the ground state orbit, m is the mass and e is the charge on the electron, ε₀ is the vacuum permittivity, the speed of the electron is:

If the nucleus $^{27}_{13}\mathrm{Al}$ has a nuclear radius of about 3.6 fermis, then $^{125}_{52}\mathrm{Te}$ would have its radius approximately as:

An alpha nucleus of energy 1/2 mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

The ionisation energy of hydrogen atom is 13.6 eV, the ionisation energy of helium atom would be: