Chapter 12: Atoms

The Balmer series for the H-atom can be observed

(a) if we measure the frequencies of light emitted when an excited atom falls to the ground state

(b) if we measure the frequencies of light emitted due to transitions between excited states and the first excited state

(c) in any transition in a H-atom

(d) as a sequence of frequencies with the higher frequencies getting closely packed

Let
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

(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

The simple Bohr model is not applicable to He⁴ atom because

(a) He⁴ is an inert gas

(b) He⁴ has neutrons in the nucleus

(c) He⁴ has one more electron

(d) electrons are not subject to central forces

The mass of an H-atom is less than the sum of the masses of a proton and electron. Why is this?

Imagine removing one electron from He⁴ and He³. Their energy levels, as worked out on the basis of Bohr model will be very close. Explain why.

When an electron falls from a higher energy to a lower energy level, the difference in the energies appears in the form of electromagnetic radiation. Why cannot it be emitted as other forms of energy?

Would the Bohr formula for the H-atom remain unchanged if proton had a charge (+4/3)e and electron a charge (−3/4)e, where e = 1.6 × 10^–19C? Give reasons for your answer.

Consider two different hydrogen atoms. The electron in each atom is in an excited state. Is it possible for the electrons to have different energies but the same orbital angular momentum according to the Bohr model?

Positronium is just like an H-atom with the proton replaced by the positively charged anti-particle of the electron (called the positron which is as massive as the electron). What would be the ground state energy of positronium?

Assume that there is no repulsive force between the electrons in an atom but the force between positive and negative charges is given by Coulomb’s law as usual. Under such circumstances, calculate the ground state energy of a He-atom.