SATHEE: dual-nature-of-radiation-and-matter Question 13

विकिरण और पदार्थ की दोहरी प्रकृति

Question: Q. 6. Two monochromatic radiations of frequencies $v_{1}$ and $v_{2} (v_{1} > v_{2})$ and having the same intensity are, in turn, incident on a photosensitive surface to cause photoelectric emission. Explain, giving reason, in which case (i) more number of electrons will be emitted and (ii) the maximum kinetic energy of the emitted photoelectrons will be more.

U] [Delhi Comptt. I, II, III 2014]

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Solution:

Ans. (i) Intensity of incident radiation $I = n h v$ , where, $n$ is the number of photons incident per unit time per unitarea. For same intensity of two monochromatic radiations of frequency $v_{1}$ and $v_{2} .1 / 2$ a) $n_{1} h v_{1} = n_{2} h v_{2}$

$\begin{array}{ll} As, & v_{1} > v_{2} \Rightarrow & n_{2} > n_{1} \end{array}$

Therefore, the number of electrons emitted for monochromatic radiation of frequency $v_{2}$ , will be more than that for radiation of frequency $v_{1}$ . $1 / 2$ $h ν = ϕ_{0} + K_{max}$

$∴$ For given $ϕ_{0}$ (work function of metal),

$K_{max}$ increases with $v$ .

$∴$ The maximum kinetic energy of emitted photoelectrons will be more for monochromatic light of frequency $v_{1} ($ as $v_{1} > v_{2})$ .

[CBSE Marking Scheme, 2014]

Detailed Answer :

(i) According to the quantum theory number of photons per unit area in unit time is the intensity of radiation.

Hence, $I = n h v$

where, $n =$ number of photons

$v =$ frequency of monochromatic radiation

Given

$\begin{aligned} I_{1} & = I_{2} n_{1} h v_{1} & = n_{2} h v_{2} \end{aligned}$

$\begin{array}{ll} if, & v_{1} > v_{2} then & n_{1} < n_{2} \end{array}$

Hence, number of photons having $v_{2}$ frequency of monochromatic radiation is more than the number of photons having $v_{1}$ frequency of monochromatic radiation.

(ii) Kinetic energy of the emitted photons is given by $K E = h v - ϕ_{0};$ where, $ϕ_{0}$ is the work function of photosensitive surface; which is same for both radiations, as it is characteristic of metal surface. $1 / 2$ So, Maximum kinetic energy of emitted photon is more for higher frequency of radiation. Hence kinetic energy of emitted photoelectrons are more with $v_{1}$ frequency of monochromatic radiation.

विकिरण और पदार्थ की दोहरी प्रकृति

Detailed Answer :

विषयसूची

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

विकिरण और पदार्थ की दोहरी प्रकृति

Detailed Answer :

विषयसूची

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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