(D) The intensity $I$ at a distance $r = 5 \ m$ from the source is given by $I = \frac{P}{4 \pi r^2}$.Substituting the values: $I = \frac{942}{4 \time

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(D) The intensity $I$ at a distance $r = 5 \ m$ from the source is given by $I = \frac{P}{4 \pi r^2}$.Substituting the values: $I = \frac{942}{4 \times 3.14 \times 5^2} = \frac{942}{12.56 \times 25} = \frac{942}{314} = 3 \ W/m^2$.The energy of a single photon is $E = \frac{hc}{\lambda} = \frac{6.6 \times 10^{-34} \times 3 \times 10^8}{660 \times 10^{-9}} = \frac{19.8 \times 10^{-26}}{6.6 \times 10^{-7}} = 3 \times 10^{-19} \ J$.The photon flux $\phi$ is the number of photons per unit area per unit time,given by $\phi = \frac{I}{E}$.$\phi = \frac{3}{3 \times 10^{-19}} = 1 \times 10^{19} \ \frac{\text{photon}}{m^2 \cdot s}$.

Class 12 Physics Dual Nature of Radiation and matter Particle Nature of Light : Photon

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$A$ lamp of power $942 \ W$ radiates energy uniformly in all directions. The wavelength of radiation is $660 \ nm$. The photon flux on a small screen $5.0 \ m$ from the lamp in units of $\frac{\text{photon}}{m^2 \cdot s}$ is (Take Planck's constant $h = 6.6 \times 10^{-34} \ J \cdot s$ and speed of light $c = 3 \times 10^8 \ m/s$)

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A
$5 \times 10^{20}$
B
$2 \pi \times 10^{19}$
C
$\frac{6}{\pi} \times 10^{18}$
D
$4 \times 10^{19}$

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Class 12

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Dual Nature of Radiation and matter

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Particle Nature of Light : Photon

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$A$ scientist claims to have a perfect technique in which he can spontaneously convert an electron completely into energy in the laboratory without any other material required. What is the conclusion about this claim from our current understanding of physics?

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The approximate wavelength of a photon of energy $2.48 \,eV$ is ............ $\mathring A$.

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The number of photons emitted from a photocell by a source placed at a distance of $0.5 \ m$ is how many times the number of photons emitted by the same source placed at a distance of $1 \ m$?

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$A$ light bulb emits $5\%$ of its energy as visible light. How many quanta are emitted per second by a $100 \ W$ lamp? (Assume the wavelength of visible light is $5.6 \times 10^{-5} \ cm$)

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If $c$ is the velocity of light in free space,the correct statements about photon among the following are:
$A$. The energy of a photon is $E=h v$.
$B$. The velocity of a photon is $c$.
$C$. The momentum of a photon,$p=\frac{h v}{c}$.
$D$. In a photon-electron collision,both total energy and total momentum are conserved.
$E$. Photon possesses positive charge.
Choose the correct answer from the options given below:

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$A$ scientist claims to have a perfect technique in which he can spontaneously convert an electron completely into energy in the laboratory without any other material required. What is the conclusion about this claim from our current understanding of physics?

The approximate wavelength of a photon of energy $2.48 \,eV$ is ............ $\mathring A$.

The number of photons emitted from a photocell by a source placed at a distance of $0.5 \ m$ is how many times the number of photons emitted by the same source placed at a distance of $1 \ m$?

$A$ light bulb emits $5\%$ of its energy as visible light. How many quanta are emitted per second by a $100 \ W$ lamp? (Assume the wavelength of visible light is $5.6 \times 10^{-5} \ cm$)

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