SATHEE: Modern Physics 2 Question 7

Modern Physics 2 Question 7

7. A metal plate of area $1 \times 10^{- 4} m^{2}$ is illuminated by a radiation of intensity $16 m W / m^{2}$ . The work function of the metal is $5 e V$ . The energy of the incident photons is $10 e V$ and only $10$ of it produces photoelectrons. The number of emitted photoelectrons per second and their maximum energy, respectively will be (Take, $1 e V = 1.6 \times 10^{- 19} J)$

(a) $10^{11}$ and $5 e V$

(b) $10^{12}$ and $5 e V$

(d) $10^{14}$ and $10 e V$

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Solution:

We know that, intensity of a radiation $I$ with energy ’ $E$ ’ incident on a plate per second per unit area is given as

$\Rightarrow I = \frac{d E}{d A \times d t} \Rightarrow \frac{d E}{d t} = I d A or I A$

i.e., energy incident per unit time $= I A$

Substituting the given values, we get

$\begin{aligned} \frac{d E}{d t} = 16 \times 10^{- 3} \times 1 \times 10^{- 4} \\ \frac{d E}{d t} = 16 \times 10^{- 7} W \end{aligned}$

Using Einstein’s photoelectric equation, we can find kinetic energy of the incident radiation as

$\begin{aligned} E = \frac{1}{2} m v^{2} + φ \\ or (Here, φ is work \\ = K E + φ \\ K E = E - φ = 10 e V - 5 e V \\ K E = 5 e V \end{aligned}$

Now, energy per unit time for incident photons will be

$\begin{aligned} ∵ & E & = N h ν \\ ∴ & \frac{d E}{d t} & = h ν \frac{d N}{d t} or h ν \dot{N} \end{aligned}$

From Eqs. (i) and (iii), we get

$\begin{aligned} h \cup \dot{N} = 16 \times 10^{- 7} or E \dot{N} = 16 \times 10^{- 7} \\ But E = 10 e V, so \\ \dot{N} (10 \times 1.6 \times 10^{- 19}) = 16 \times 10^{- 7} \Rightarrow \dot{N} = 10^{12} \end{aligned}$

$∵$ Only $10$ of incident photons emit electrons.

So, emitted electrons per second are

$\frac{10}{100} \times 10^{12} = 10^{11}$

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Modern Physics 2 Question 7

Solution:

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एनसीईआरटी व्यायाम वीडियो समाधान

Modern Physics 2 Question 7

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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