A source of light emits monochromatic visible light of wavelength 500 nm. The source emits light of power 100W. The number of photons emitted per sec of the visible light of the given wavelength is: <math> <mo>(</mo> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">c</mi> <mo>=</mo> <mn>1240</mn> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">V</mi> <mo>.</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">m</mi> <mo>)</mo> </math>

Photon energy = h c λ = 1240 e V . n m 500 n m = 2.48 e V = 2.48 × 1.6 × 10 - 19 J = 4 × 10 - 19 J No. of photons emitted per sec = power photon Energy = 100 4 × 10 - 19 s - 1 = 2.5 × 10 20 s - 1

A source of light emits monochromatic visible light of wavelength 500 nm. The source emits light of power 100W. The number of photons emitted per sec of the visible light of the given wavelength is: <math> <mo>(</mo> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">c</mi> <mo>=</mo> <mn>1240</mn> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">V</mi> <mo>.</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">m</mi> <mo>)</mo> </math> &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

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Physics Class 12th Dual Nature of Radiation and Matter

A source of light emits monochromatic visible light of wavelength 500 nm. The source emits light of power 100W. The number of photons emitted per sec of the visible light of the given wavelength is: $(h c = 1240 e V . n m)$

Option 1 -

$2.5 * 10^{19}$

Option 2 -

$5.0 * 10^{19}$

Option 3 -

$4.5 * 10^{20}$

Option 4 -

$2.5 * 10^{20}$

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1 Answer

Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 4

Detailed Solution:

Photon energy $\frac{}{} \frac{}{}^{}^{}$ $= \frac{h c}{λ} = \frac{1240 e V . n m}{500 n m} = 2.48 e V = 2.48 \times 1.6 \times 10^{- 19} J = 4 \times 10^{- 19} J$

No. of photons emitted per sec $= \frac{power}{photon Energy} = \frac{100}{4 \times 10^{- 19}} s^{- 1} = 2.5 \times 10^{20} s^{- 1}$

Photon energy <math><mfrac><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></mfrac><mfrac><mrow><mrow></mrow></mrow><mrow><mrow><mtext></mtext></mrow></mrow></mfrac><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup><mtext></mtext><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup><mtext></mtext></math> <math> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>h</mi> <mi>c</mi> </mrow> </mrow> <mrow> <mrow> <mi>λ</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1240</mn> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">V</mi> <mo>.</mo> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow> <mrow> <mn>500</mn> <mtext> </mtext> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>2.48</mn> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">V</mi> <mo>=</mo> <mn>2.48</mn> <mo>×</mo> <mn>1.6</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>19</mn> </mrow> </mrow> </msup> <mtext> </mtext> <mi mathvariant="normal">J</mi> <mo>=</mo> <mn>4</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>19</mn> </mrow> </mrow> </msup> <mtext> </mtext> <mi mathvariant="normal">J</mi> </math> No. of photons emitted per sec <math> <mo>=</mo> <mfrac> <mrow> <mrow> <mtext> </mtext> <mtext>power</mtext> <mtext> </mtext> </mrow> </mrow> <mrow> <mrow> <mtext> </mtext> <mtext>photon Energy</mtext> <mtext> </mtext> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>100</mn> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>19</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> <msup> <mrow> <mrow> <mi>s</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </msup> <mo>=</mo> <mn>2.5</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>20</mn> </mrow> </mrow> </msup> <msup> <mrow> <mrow> <mi>s</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </msup> </math>

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A source of light emits monochromatic visible light of wavelength 500 nm. The source emits light of power 100W. The number of photons emitted per sec of the visible light of the given wavelength is: $(h c = 1240 e V . n m)$

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A source of light emits monochromatic visible light of wavelength 500 nm. The source emits light of power 100W. The number of photons emitted per sec of the visible light of the given wavelength is: ( h c = 1240 e V . n m )

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A source of light emits monochromatic visible light of wavelength 500 nm. The source emits light of power 100W. The number of photons emitted per sec of the visible light of the given wavelength is: $(h c = 1240 e V . n m)$