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NEET Chemistry
QUESTION #7369
Question 1
A particle moves at 3 times the speed of an electron. If the ratio of de Broglie wavelength of the particle to that of the electron is \(1.8 \times 10^{-4}\), the particle is:
Correct Answer Explanation
de Broglie wavelength: \(\lambda = \dfrac{h}{mv}\)
\(\dfrac{\lambda_p}{\lambda_e} = \dfrac{m_e v_e}{m_p v_p} = \dfrac{m_e}{m_p \times 3} = 1.8 \times 10^{-4}\)
\(m_p = \dfrac{m_e}{3 \times 1.8 \times 10^{-4}} = \dfrac{9.1 \times 10^{-31}}{5.4 \times 10^{-4}} \approx 6.68 \times 10^{-27}\) kg
This is approximately 4 times the proton mass, matching the \(\alpha\)-particle (He nucleus, mass \(\approx 4\) u).
\(\dfrac{\lambda_p}{\lambda_e} = \dfrac{m_e v_e}{m_p v_p} = \dfrac{m_e}{m_p \times 3} = 1.8 \times 10^{-4}\)
\(m_p = \dfrac{m_e}{3 \times 1.8 \times 10^{-4}} = \dfrac{9.1 \times 10^{-31}}{5.4 \times 10^{-4}} \approx 6.68 \times 10^{-27}\) kg
This is approximately 4 times the proton mass, matching the \(\alpha\)-particle (He nucleus, mass \(\approx 4\) u).
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