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JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of \(100\, V\). What should nearly be the ratio of their wavelengths ? \(\left( m _{ P }=1.00727\, u , m _{ e }=0.00055 \,u \right)\)
- A \(1860: 1\)
- B \((1860)^{2}: 1\)
- C \(41.4: 1\)
- D \(43: 1\)
Answer & Solution
Correct Answer
(D) \(43: 1\)
Step-by-step Solution
Detailed explanation
\(\lambda=\frac{ h }{ mv }=\frac{ h }{\sqrt{2 mK }}=\frac{ h }{\sqrt{2 mqV }}\) \(\frac{\lambda_{1}}{\lambda_{2}}=\sqrt{\frac{ m _{2}}{ m _{1}}}\) \(\frac{\lambda_{ e }}{\lambda_{ P }}=\sqrt{\frac{ m _{ P }}{ m _{ e }}}=\sqrt{1831.4}=42.79\)
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