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Answer the following questions:
(a) Quarks inside protons and neutrons are thought to carry fractional charges $[(+2 / 3) e ;(-1 / 3) e]$. Why do they not show up in Millikan's oil-drop experiment?
(b) What is so special about the combination $\mathrm{e} / \mathrm{m}$ ? Why do we not simply talk of e and $m$ 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 $\mathbf{E}=\mathrm{h} \boldsymbol{v}, \mathrm{p}=\frac{\mathrm{h}}{\lambda}$
But while the value of $\lambda$ is physically significant, the value of $v$ (and therefore, the value of the phase speed $v \lambda$ ) has no physical significance. Why?
(a) Quarks inside protons and neutrons are thought to carry fractional charges $[(+2 / 3) e ;(-1 / 3) e]$. Why do they not show up in Millikan's oil-drop experiment?
(b) What is so special about the combination $\mathrm{e} / \mathrm{m}$ ? Why do we not simply talk of e and $m$ 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 $\mathbf{E}=\mathrm{h} \boldsymbol{v}, \mathrm{p}=\frac{\mathrm{h}}{\lambda}$
But while the value of $\lambda$ is physically significant, the value of $v$ (and therefore, the value of the phase speed $v \lambda$ ) has no physical significance. Why?
Solution:
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Verified Answer
(a) Quarks have fractional charges that are confined within a $\mathrm{p}^{+}$or $\mathrm{n}^0$. They are bound by nuclear forces which are strong and grow stronger if quarks are tried to pull apart. Thus quarks always remain together in form of fractional changes inside $\mathrm{p}^{+}$, $n^0$ only.
(b) The motion of $\mathrm{e}$ - inside electric and magnetic field is given by $\mathrm{eV}=\frac{1}{2} \mathrm{mv}^2$ and $\mathrm{eE}=\mathrm{ma}$ and $\mathrm{BeV}=$ $\frac{\mathrm{mv}^2}{\mathrm{r}}$. All these equations involve e and $\mathrm{m}$ together but not separately.
(c) Gases are generally insulators at atmospheric pressures because even if they are ionised, their positive and negative ions are close together and get ionised to form neutral atoms. At low pressures, the ionised gas particles are far apart and cannot recombine, hence they are free to conduct. Due to the presence of such free ions, gas can conduct.
(d) This is because work function gives the minimum energy required for the uppermost $\mathrm{e}^{-}$of the conduction band (least ionisation potential) to come out of the metal. Not all electrons ejected are from this level but from a different levels which requires different energy to come out. Hence, for same radiation incident, electrons may be knocked off from different levels and come out with different energy.
(e) The absolute value of energy E (only numerical part) has no significance except as an additive constant (P.S.- the sign of energy has physical meaning) put with momentum it is not so, Similarly for matter waves frequency has no direct physical meaning but wavelength is physically significant. The phase speed $v_\lambda=\mathrm{v}$ has no significance but group speed $=\frac{\mathrm{dE}}{\mathrm{dp}}=\frac{\mathrm{p}}{\mathrm{m}}$ has significance physically.
(b) The motion of $\mathrm{e}$ - inside electric and magnetic field is given by $\mathrm{eV}=\frac{1}{2} \mathrm{mv}^2$ and $\mathrm{eE}=\mathrm{ma}$ and $\mathrm{BeV}=$ $\frac{\mathrm{mv}^2}{\mathrm{r}}$. All these equations involve e and $\mathrm{m}$ together but not separately.
(c) Gases are generally insulators at atmospheric pressures because even if they are ionised, their positive and negative ions are close together and get ionised to form neutral atoms. At low pressures, the ionised gas particles are far apart and cannot recombine, hence they are free to conduct. Due to the presence of such free ions, gas can conduct.
(d) This is because work function gives the minimum energy required for the uppermost $\mathrm{e}^{-}$of the conduction band (least ionisation potential) to come out of the metal. Not all electrons ejected are from this level but from a different levels which requires different energy to come out. Hence, for same radiation incident, electrons may be knocked off from different levels and come out with different energy.
(e) The absolute value of energy E (only numerical part) has no significance except as an additive constant (P.S.- the sign of energy has physical meaning) put with momentum it is not so, Similarly for matter waves frequency has no direct physical meaning but wavelength is physically significant. The phase speed $v_\lambda=\mathrm{v}$ has no significance but group speed $=\frac{\mathrm{dE}}{\mathrm{dp}}=\frac{\mathrm{p}}{\mathrm{m}}$ has significance physically.
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