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

Question

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 (A)  m1/m2  (B)  m2/m1  (C) 1 (D)  √m2/√m1

Tardigrade Admin · Accepted Answer

From law of conservation of momentum, P1 = P2 (in opposite directions) Now de-Broglie wavelength is given by λ = (h/p), where h = Planck's constant Since magnitude of momentum (p) of both the particles is equal, therefore λ1 = λ2 or λ1/ λ2 = 1

Q. A particle of mass M at rest decays into two particles of
masses $m_{1} an d m_{2}$ having non-zero velocities.
The ratio of the de-Broglie wavelengths of the particles
$\frac{λ _{1}}{λ _{2}}$ is

$m_{1} / m_{2}$

$m_{2} / m_{1}$

1

$m_{2} / m_{1}$

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 $λ_{1} / λ_{2} = 1$

Q. A particle of mass M at rest decays into two particles of masses m1​andm2​ having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles λ2​λ1​​ is

m1​/m2​

m2​/m1​

1

m2​​/m1​​

From law of conservation of momentum, P1​=P2​ (in opposite directions) Now de-Broglie wavelength is given by λ=ph​, where h = Planck's constant Since magnitude of momentum (p) of both the particles is equal, therefore λ1​=λ2​ or λ1​/λ2​=1

Q. A particle of mass M at rest decays into two particles of
masses $m_{1} an d m_{2}$ having non-zero velocities.
The ratio of the de-Broglie wavelengths of the particles
$\frac{λ _{1}}{λ _{2}}$ is

$m_{1} / m_{2}$

$m_{2} / m_{1}$

$m_{2} / m_{1}$

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 $λ_{1} / λ_{2} = 1$