SATHEE: Modern Physics 2 Question 37

Modern Physics 2 Question 37

36. A beam of light has three wavelengths $4144 \AA, 4972 \AA$ and $6216 \AA$ with a total intensity of $3.6 \times 10^{- 3} W m^{- 2}$ equally distributed amongst the three wavelengths. The beam falls normally on an area $1.0 c m^{2}$ of a clean metallic surface of work function $2.3 e V$ . Assume that there is no loss of light by reflection and that each energetically capable photon ejects one electron. Calculate the number of photoelectrons liberated in two seconds.

(1989, 8M)

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Solution:

Energy of photon having wavelength $4144 \AA$ ,

$E_{1} = \frac{12375}{4144} e V = 2.99 e V$

Similarly, $E_{2} = \frac{12375}{4972} e V = 2.49 e V$ and

$E_{3} = \frac{12375}{6216} e V = 1.99 e V$

Since, only $E_{1}$ and $E_{2}$ are greater than the work function $W = 2.3 e V$ , only first two wavelengths are capable for ejecting photoelectrons. Given intensity is equally distributed in all wavelengths. Therefore, intensity corresponding to each wavelength is

$\frac{3.6 \times 10^{- 3}}{3} = 1.2 \times 10^{- 3} W / m^{2}$

Or energy incident per second in the given area ( $A = 1.0 c m^{2} = 10^{- 4} m^{2})$ is

$\begin{aligned} ρ & = 1.2 \times 10^{- 3} \times 10^{- 4} \\ = 1.2 \times 10^{- 7} J / s \end{aligned}$

Let $n_{1}$ be the number of photons incident per unit time in the given area corresponding to first wavelength. Then

$\begin{aligned} n_{1} & = \frac{ρ}{E_{1}} = \frac{1.2 \times 10^{- 7}}{2.99 \times 1.6 \times 10^{- 19}} \\ = 2.5 \times 10^{11} \end{aligned}$

Similarly, $n_{2} = \frac{ρ}{E_{2}} = \frac{1.2 \times 10^{- 7}}{2.49 \times 1.6 \times 10^{- 19}}$

$= 3.0 \times 10^{11}$

Since, each energetically capable photon ejects electron, total number of photoelectrons liberated in $2 s$ .

$\begin{aligned} = 2 (n_{1} + n_{2}) = 2 (2.5 + 3.0) \times 10^{11} \\ = 1.1 \times 10^{12} \end{aligned}$

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Modern Physics 2 Question 37

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

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अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Modern Physics 2 Question 37

Solution:

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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