THE de Broglie wavelength for an electron and a photon are $λ_{e} a n d λ_{p}$ respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two

Option 1 -

$λ_{p}$ ∝ $λ_{e}^{2}$

Option 2 -

$λ_{p}$ ∝ $λ_{e}$

Option 3 -

$λ_{p}$ ∝ $\sqrt[]{λ_{e}}$

Option 4 -

$λ_{p}$ ∝ $\sqrt[]{\frac{1}{λ_{e}}}$

3 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

$λ_{e} = \frac{h}{P_{e}} = \frac{h}{\sqrt[]{2 m_{e} K_{e}}} \Rightarrow λ_{e}^{2} = \frac{h^{2}}{2 m_{e} k_{e}} \Rightarrow K_{e} = \frac{h^{2}}{2 m_{e} λ_{e}^{2}}$ - (i)

$λ_{P} = \frac{h}{P_{P}} = \frac{h c}{K_{P}} \Rightarrow K_{P} = \frac{h c}{λ_{P}}$ - (ii)

K_e = K_P

$\Rightarrow λ_{P} α λ_{e}^{2}$

<!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1813753726"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>e</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <mroot> <mrow> <mn>2</mn> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mi>e</mi> </mrow> </msub> <msub> <mrow> <mi>K</mi> </mrow> <mrow> <mi>e</mi> </mrow> </msub> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> <mo>⇒</mo> <msubsup> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>e</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mi>e</mi> </mrow> </msub> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mi>e</mi> </mrow> </msub> </mrow> </mfrac> <mo>⇒</mo> <msub> <mrow> <mi>K</mi> </mrow> <mrow> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mi>e</mi> </mrow> </msub> <msubsup> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>e</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> </math>    - (i) <math> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> <mi>c</mi> </mrow> <mrow> <msub> <mrow> <mi>K</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> </mrow> </mfrac> <mo>⇒</mo> <msub> <mrow> <mi>K</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> <mi>c</mi> </mrow> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </math>     - (ii)Ke = KP <math> <mrow> <mo>⇒</mo> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> <mi>α</mi> <msubsup> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>e</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </math>         <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1813753728"> </o:OLEObject></xml><! [endif]->

0 Upvotes 0 Downvotes

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
688k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

THE de Broglie wavelength for an electron and a photon are $λ_{e} a n d λ_{p}$ respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two

1 Answer

Learn more about...

Most viewed information

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

THE de Broglie wavelength for an electron and a photon are λ e a n d λ p respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two

1 Answer

Learn more about...

Most viewed information

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

THE de Broglie wavelength for an electron and a photon are $λ_{e} a n d λ_{p}$ respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two