Question 178: Dual Nature of Matter and Radiation

Question

The de-Broglie wavelength of a proton and $$\alpha$$-particle are equal. The ratio of their velocities is :

Accepted Answer

Let $$\lambda$$
p
, $$\lambda$$
$$\alpha$$
, m
p
, m
$$\alpha$$
, v
p
, v
$$\alpha$$
, p
p
and p
$$\alpha$$
be the wavelength, mass, velocity and momentum of proton and $$\alpha$$-particle, respectively.
Given, $$\lambda$$
p
= $$\lambda$$
$$\alpha$$
As we know that,
$$\lambda$$ = h/p
$$	herefore$$ $${h \over {{p_p}}} = {h \over {{p_\alpha }}}$$
$$\Rightarrow$$ p
p
= p
$$\alpha$$
$$\Rightarrow$$ m
p
v
p
= m
$$\alpha$$
v
$$\alpha$$
$$\Rightarrow$$ m
p
v
p
= 4m
p
v
$$\alpha$$
($$\because$$ m
$$\alpha$$
= 4m
p
)
$$\Rightarrow$$ $${{{v_p}} \over {{v_\alpha }}} = {4 \over 1}$$ or 4 : 1

Answer

4 : 2

Answer

4 : 3

Answer

4 : 1

Answer

1 : 4

Dual Nature of Matter and Radiation

The de-Broglie wavelength of a proton and $\alpha$-particle are equal. The ratio of their velocities is :

Choose the correct answer: