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Particle A has mass m and charge q, accelerated through potential difference 50 V. Particle B has mass 4m and charge q, accelerated through potential difference 2500 V. Find the ratio of their de-Broglie wavelengths lambda_A / lambda_B.
- 10.00
- 14.14
- 4.47
- 0.07
Correct answer: 14.14
Solution
lambda = h/sqrt(2mqV). Ratio = sqrt((m_B*V_B)/(m_A*V_A)) since q is the same. = sqrt((4m * 2500)/(m * 50)) = sqrt(10000/50) = sqrt(200) = 10*sqrt(2) ≈ 14.14.
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