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JEE Mains · Physics · STD 12 - Dual nature of radiation and matter
- JEE Mains 2019
- Medium
- MCQ
If the deBroglie wavelength of an electron is equal to \(10^{-3}\) times the wavelength of a photon of frequency \(6\,\times 10^{14}\,Hz,\) then the speed of electron is equal to: (Speed of light \(=3\times 10^8\,m/s\,;\) Planck’s constant \(=6.63\times 10^{-34}\,J.s\,;\) Mass of electron \(=9.1\times 10^{-31}\,kg\) )
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(1.45\times 10^6\,m/s\)
Step-by-step Solution
Detailed explanation
\({\lambda _e} = {\lambda _{{\text{photon }}}} \times {10^{ - 3}}\)
\( \Rightarrow \frac{h}{{mv}} = \frac{c}{v} \times {10^{ - 3}}{\text{s}}\)
\( \Rightarrow v = \frac{{hv}}{{mC \times {{10}^{ - 3}}}}\)
\( = \frac{{6.62 \times {{10}^{ - 34}} \times 6 \times {{10}^{14}}}}{{9.1 \times {{10}^{ - 31}} \times 3 \times {{10}^8} \times {{10}^{ - 3}}}}\)
\( = 1.45 \times {10^6}\)
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