SATHEE: Modern Physics 4 Question 18

Modern Physics 4 Question 18

18. A particle of mass $M$ at rest decays into two particles of masses $m_{1}$ and $m_{2}$ having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles $λ_{1} / λ_{2}$ is $(1999, 2 M)$

(a) $m_{1} / m_{2}$

(b) $m_{2} / m_{1}$

(d) $\sqrt{m_{2}} / \sqrt{m_{1}}$

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Solution:

From law of conservation of momentum,

$p_{1} = p_{2} (in opposite directions)$

Now de-Broglie wavelength is given by

$λ = \frac{h}{p}, where h = Planck’s constant$

Since magnitude of momentum $(p)$ of both the particles is equal, therefore $λ_{1} = λ_{2}$ or $λ_{1} / λ_{2} = 1$

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Modern Physics 4 Question 18

18. A particle of mass M at rest decays into two particles of masses m1 and m2 having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles λ1/λ2 is (1999,2M)

Solution:

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18. A particle of mass $M$ at rest decays into two particles of masses $m_{1}$ and $m_{2}$ having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles $λ_{1} / λ_{2}$ is $(1999, 2 M)$