The de Broglie wavelength associated with a moving particle is inversely proportional to its:
A. Momentum
B. Kinetic energy
C. Velocity only
D. Mass only
Answer: Option A
Solution (By JKSSB Mock Tests)
Louis de Broglie proposed that matter exhibits wave-like properties. The de Broglie wavelength (lambda) of a particle is given by the formula lambda = h / p, where 'h' is Planck's constant and 'p' is the linear momentum (mass * velocity) of the particle. Therefore, the wavelength is strictly inversely proportional to the momentum of the moving particle.
Explanation:
After n half-lives, activity reduces to (1/2)ⁿ of initial. Set (1/2)ⁿ = 1/16 ⇒ (1/2)ⁿ = (1/2)⁴ ⇒ n = 4 half-lives. Thus time = 4 × half-life. Memory aid: '1/2ⁿ remaining after n half-lives; 1/16 = 1/2⁴ ⇒ 4 half-lives'. This radioactivity calculation is frequently tested in competitive exams. Always express fraction as power of 1/2 to find half-life count. This problem assesses understanding of exponential decay without heavy computation.
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