TS EAMCET · Physics · Dual Nature of Matter
If a proton is accelerated through a potential difference of \(1000 \mathrm{~V}\), then its de-Broglie wavelength is (given, \(m_p=1.67 \times 10^{-27} \mathrm{~kg}\), \(\left.h=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}\right)\)
- A \(9.1 \times 10^{13} \mathrm{~m}\)
- B \(9.1 \times 10^{+13} \mathrm{~m}\)
- C \(1.09 \times 10^{15} \mathrm{~m}\)
- D \(1.09 \times 10^{+15} \mathrm{~m}\)
Answer & Solution
Correct Answer
(A) \(9.1 \times 10^{13} \mathrm{~m}\)
Step-by-step Solution
Detailed explanation
\(\lambda_{\text {proton }}=\frac{h}{p}=\frac{0.286}{\sqrt{V}}(Å)\) (This formula is for protons.) \[ \therefore \quad \lambda=\frac{0.286}{\sqrt{1000}} \times 10^{-10} \mathrm{~m} \approx 9.1 \times 10^{-13} \mathrm{~m} \]
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