Physics Class 12 NCERT Solutions: Chapter 11 Dual Nature of Radiation and Matter Part 17 (For CBSE, ICSE, IAS, NET, NRA 2022)

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DeBroglie Hypothesis

Q: 36. Compute the typical de Broglie wavelength of an electron in a metal at and compare it with the mean separation between two electrons in a metal, which is given to be about .

[Note: Exercises 35 (Reference: Chapter 11 Dual Nature of Radiation and Matter Part 16) and 36 reveal that while the wave-packets associated with gaseous molecules under ordinary conditions are non-overlapping, the electron wave-packets in a metal strongly overlap with one another. This suggests that whereas molecules in an ordinary gas can be distinguished apart, electrons in a metal cannot be distinguished apart from one another. This in distinguish ability has many fundamental implications which you will explore in more advanced Physics courses.]

Answer:

Temperature,

Mean separation between two electrons,

De Broglie wavelength of an electron is given as:

Where,

Hence, the de Broglie wavelength is much greater than the given inter-electron separation.

Q: 37. Answer the following questions:

(A) Quarks inside protons and neutrons are thought to carry fractional charges . Why do they not show up in Millikan՚s oil-drop experiment?

(B) What is so special about the combination e/m? Why do we not simply talk of and separately?

(C) Why should gases be insulators at ordinary pressures and start conducting at very low pressures?

(D) Every metal has a definite work function. Why do all photoelectrons not come out with the same energy if incident radiation is monochromatic? Why is there an energy distribution of photoelectrons?

(E) The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:

But while the value of is physically significant, the value of (and therefore, the value of the phase speed ) has no physical significance. Why?

Answer:

(A) Quarks inside protons and neutrons carry fractional charges. This is because nuclear force increases extremely if they are pulled apart. Therefore, fractional charges may exist in nature; observable charges are still the integral multiple of an electrical charge.

(B) The basic relations for electric field and magnetic field are

Respectively

These relations include and B (magnetic field) . These relations give the value of velocity of an electron as and

Respectively.

It can be observed from these relations that the dynamics of an electron is determined not by e and m separately, but by the ratio .

(C) At atmospheric pressure, the ions of gases have no chance of reaching their respective electrons because of collision and recombination with other gas molecules. Hence, gases are insulators at atmospheric pressure. At low pressures, ions have a chance of reaching their respective electrodes and constitute a current. Hence, they conduct electricity at these pressures.

(D) The work function of a metal is the minimum energy required for a conduction electron to get out of the metal surface. All the electrons in an atom do not have the same energy level. When a ray having some photon energy is incident on a metal surface, the electrons come out from different levels with different energies. Hence, these emitted electrons show different energy distributions.

(E) The absolute value of energy of a particle is arbitrary within the additive constant. Hence, wavelength is significant, but the frequency (v) associated with an electron has no direct physical significance.

Therefore, the product (phase speed) has no physical significance.

Group speed is given as:

This quantity has a physical meaning.