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Physics · 2022 · 3 marks
Dual Nature of Radiation and MatterEinstein’s Photoelectric Equation: Energy Quantum of Radiation3 marksApplyshort answer
CBSE 2022 · Region 4 · Set 1 · Q9
(a) Use Einstein's photoelectric equation to depict the variation of the maximum kinetic energy ( E_k ) of electrons emitted, with the frequency ( v…
(a)
Use Einstein's photoelectric equation to depict the variation of the maximum kinetic energy ( $\displaystyle \mathrm{E}_{\mathrm{k}}$ ) of electrons emitted, with the frequency ( $\displaystyle v$ ) of the incident radiation.
(b)
A photosensitive surface is illuminated with a beam of (i) yellow light, and (ii) red light, both of the same intensity. In which case will
(I)
photoelectrons have more $\displaystyle \mathrm{E}_{\mathrm{k}}$?
(II)
more numbers of electrons be emitted? Justify your answer in each case.
Marking-scheme solution
(a) Maximum kinetic energy vs frequency graph $\displaystyle 1$
(b) (I) Justification for more $\displaystyle \mathrm{E}_{\mathrm{K}} \quad 1$
(II) Justification for more number of emission of electron $\displaystyle 1$
(a)
(b) (I)
$$\mathrm{E}_{\mathrm{K}}=\mathrm{h} v-\phi_{0}
$$
as
$$v_{\mathrm{Y}}>v_{\mathrm{R}}
$$
$$\left(E_{K}\right)_{y}>\left(\mathrm{E}_{K}\right)_{R}
$$
For a given photosensitive surface, K.E. of photo-electrons will be more for yellow light.
(II) Since the number of photons incident on unit area per unit time for same intensity of two lights will be more in Red light $\displaystyle \left(\mathrm{N}_{\mathrm{R}}>\mathrm{N}_{\mathrm{Y}}\right)$ hence more number of photoelectrons will be ejected for Red light.
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