Question 199: Dual Nature of Matter and Radiation

Question

A nucleus A, with a finite de-broglie
wavelength $$\lambda $$A, undergoes spontaneous fission
into two nuclei B and C of equal mass. B flies
in the same direction as that of A, while C flies
in the opposite direction with a velocity equal
to half of that of B. The de-Broglie wavelengths
$$\lambda $$B and $$\lambda $$C of B and C are respectively :

Accepted Answer

Let mass of B and C is m each. By momentum conservation
$$2m{v_0} = mv - {{mv} \over 2}$$
v = 4v
0
P
A
= 2mv
0
pB = 4mv
0
pc = 2mv
0
De-Broglie wavelength $$\lambda  = {h \over p}$$
$${\lambda _A} = {h \over {2m{v_0}}}$$; $${\lambda _B} = {h \over {4m{v_0}}}$$; $${\lambda _C} = {h \over {2m{v_0}}}$$

Answer

$$\lambda $$A, 2$$\lambda $$A

Answer

2$$\lambda $$A, $$\lambda $$A

Answer

$$\lambda $$A, $$\lambda $$A/2

Answer

$$\lambda $$A/2, $$\lambda $$A

Dual Nature of Matter and Radiation

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