NCERT Physics Class 12 Exemplar Ch 12 Atoms Part 2

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Short Answer

19 Positronium is just like a 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?

Ans:

The ‘m’ that occurs in the Bohr formula is the reduced mass. For H-atom , For Positronium . Hence for a Positronium

20 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.

Ans:

  • For a nucleus with charge 2e and electrons of charge –e, the levels are .

  • The ground state will have two electrons each of energy E, and the total ground state energy would by

21 Using Bohr model, calculate the electric current created by the electron when the H-atom is in the ground state.

Ans:

velocity of electron

Bohr radius.

Number of revolutions per unit time

22 Show that the first few frequencies of light that is emitted when electrons fall to the level from levels higher than , are approximate harmonics (i.e. in the ratio 1: 2: 3...) when .

Ans:

Where and R is Rydberg constant.

For

Thus, are approximately in the order

23 What is the minimum energy that must be given to a H atom in ground state so that it can emit an line in Balmer series. If the angular momentum of the system is conserved, what would be the angular momentum of such photon?

Ans:

  • in Balmer series corresponds to transition to . So the electron in ground state n = 1 must first be put in state .

  • Energy required .

  • If angular momentum is conserved, angular momentum of photon = change in angular momentum of electron

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