NEET · Physics · STD 12 - 11. Dual nature of radiation and matter
A photon and an electron (mass \(m\) ) have the same energy \(E\). The ratio ( \(\lambda_{\text {photon }} / \lambda_{\text {electron }}\) ) of their de Broglie wavelengths is: ( c is the speed of light)
- A \(\sqrt{\text E / 2\text{ m}}\)
- B \(\text c \sqrt{2 \text{mE} }\)
- C \(\text c \sqrt{\frac{2\text{ m}}{\text E}}\)
- D \(\frac{1}{\text c} \sqrt{\text E / 2\text m}\)
Answer & Solution
Correct Answer
(C) \(\text c \sqrt{\frac{2\text{ m}}{\text E}}\)
Step-by-step Solution
Detailed explanation
Photon & electron have same energy E
\(\frac{\lambda_{\text {photon }}}{\lambda_{\text {electron }}}=\frac{\frac{h c}{ E }}{\frac{h}{\sqrt{2 mE }}}=c \sqrt{\frac{2 m}{ E }}\)
\(\frac{\lambda_{\text {photon }}}{\lambda_{\text {electron }}}=\frac{\frac{h c}{ E }}{\frac{h}{\sqrt{2 mE }}}=c \sqrt{\frac{2 m}{ E }}\)
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