Question:
According to de-Broglie hypothesis, the ratio of the wave-length of a photon and that of an electron having same energy 'E' is (m = mass of electron, c = velocity of light)
According to de-Broglie hypothesis, the ratio of the wave-length of a photon and that of an electron having same energy 'E' is (m = mass of electron, c = velocity of light)
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Photon: lambda = hc/E. Electron: lambda = h / sqrt(2 m E).
Updated On: Oct 1, 2026
- \(\frac{1}{C}\sqrt{\frac{E}{2m}}\)
- \(C\sqrt{\frac{E}{2m}}\)
- \(C\sqrt{\frac{2m}{E}}\)
- \(\sqrt{\frac{2mC}{E}}\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
For a photon of energy \(E\): \(\lambda_p=\dfrac{hc}{E}\). For an electron with kinetic energy \(E\): \(p=\sqrt{2mE}\), so \(\lambda_e=\dfrac{h}{\sqrt{2mE}}\).
Step 2: Take the ratio:
\[ \dfrac{\lambda_p}{\lambda_e}=\dfrac{hc/E}{h/\sqrt{2mE}}=\dfrac{c\sqrt{2mE}}{E}=c\sqrt{\dfrac{2m}{E}} \]
Option C.
Step 3: Why the other options are wrong.
Options A and B have \(\dfrac{E}{2m}\) inside the root, which gives the inverse ratio. Option D has \(c\) inside the root, which would give the wrong dimensions.
Final Answer:
The ratio is c sqrt(2m / E). \[ \boxed{\text{(C) }c\sqrt{\dfrac{2m}{E}}} \]
For a photon of energy \(E\): \(\lambda_p=\dfrac{hc}{E}\). For an electron with kinetic energy \(E\): \(p=\sqrt{2mE}\), so \(\lambda_e=\dfrac{h}{\sqrt{2mE}}\).
Step 2: Take the ratio:
\[ \dfrac{\lambda_p}{\lambda_e}=\dfrac{hc/E}{h/\sqrt{2mE}}=\dfrac{c\sqrt{2mE}}{E}=c\sqrt{\dfrac{2m}{E}} \]
Option C.
Step 3: Why the other options are wrong.
Options A and B have \(\dfrac{E}{2m}\) inside the root, which gives the inverse ratio. Option D has \(c\) inside the root, which would give the wrong dimensions.
Final Answer:
The ratio is c sqrt(2m / E). \[ \boxed{\text{(C) }c\sqrt{\dfrac{2m}{E}}} \]
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