A certain metallic surface is illuminated by monochromatic radiation of wavelength $λ .$ The stopping potential for photoelectric current for this radiation is 3V₀. If the same surface is illuminated with a radiation of wavelength $2 λ,$ the stopping potential is V₀. The threshold wavelength of this surface for photoelectric effect is_________ $λ .$

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Let the work function of metal is $?$ , so

$k_{1} = 3 V_{0} e = \frac{h c}{λ} - ?$ . (i)

$K_{2} = V_{0} e = \frac{h c}{2 λ} - ?$ . (ii)

Doing (i) – 3 X (ii), we have

$0 = \frac{h c}{λ} - \frac{3 h c}{2 λ} + 2 ? \Rightarrow ? = \frac{h c}{4 λ}$

The threshold wavelength = $\frac{h c}{?} = 4 λ$

Let the work function of metal is <math> <mrow> <mi>? </mi> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816155966"> </o:OLEObject></xml><! [endif]->, so <math> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>3</mn> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mi>e</mi> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> <mi>c</mi> </mrow> <mrow> <mi>λ</mi> </mrow> </mfrac> <mo>−</mo> <mi>? </mi> </mrow> </math> . (i)<img > <math> <mrow> <msub> <mrow> <mi>K</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mi>e</mi> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> <mi>c</mi> </mrow> <mrow> <mn>2</mn> <mi>λ</mi> </mrow> </mfrac> <mo>−</mo> <mi>? </mi> </mrow> </math> . (ii)Doing (i) – 3 X (ii), we have <math> <mrow> <mn>0</mn> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> <mi>c</mi> </mrow> <mrow> <mi>λ</mi> </mrow> </mfrac> <mo>−</mo> <mfrac> <mrow> <mn>3</mn> <mi>h</mi> <mi>c</mi> </mrow> <mrow> <mn>2</mn> <mi>λ</mi> </mrow> </mfrac> <mo>+</mo> <mn>2</mn> <mi>? </mi> <mo>⇒</mo> <mi>? </mi> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> <mi>c</mi> </mrow> <mrow> <mn>4</mn> <mi>λ</mi> </mrow> </mfrac> </mrow> </math>    <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1816155969"> </o:OLEObject></xml><! [endif]->The threshold wavelength = <math> <mrow> <mfrac> <mrow> <mi>h</mi> <mi>c</mi> </mrow> <mrow> <mi>? </mi> </mrow> </mfrac> <mo>=</mo> <mn>4</mn> <mi>λ</mi> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1816155970"> </o:OLEObject></xml><! [endif]->

0 Upvotes 0 Downvotes

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question