A homogeneous ball (mass = $$m$$) of ideal black material at rest is illuminated with a radiation having a set of photons (wavelength = $$\lambda $$), each with the same momentum and the same energy. The rate at which photons fall on the ball is $$n.$$ The linear acceleration of the ball is
A.
$$\frac{{m\lambda }}{{nh}}$$
B.
$$\frac{{nh}}{{m\lambda }}$$
C.
$$\frac{{2nh}}{{m\lambda }}$$
D.
$$\frac{{2m\lambda }}{{nh}}$$
Answer :
$$\frac{{nh}}{{m\lambda }}$$
Solution :
Momentum imparted per unit time $$= np$$
$$\eqalign{
& \Rightarrow F = \frac{{nh}}{\lambda } \cr
& \therefore {\text{Acceleration}} = \frac{{nh}}{{m\lambda }} \cr} $$
Releted MCQ Question on Modern Physics >> Dual Nature of Matter and Radiation
Releted Question 1
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, $$\frac{{{\lambda _1}}}{{{\lambda _2}}},$$ is
A proton has kinetic energy $$E = 100\,keV$$ which is equal to that of a photon. The wavelength of photon is $${\lambda _2}$$ and that of proton is $${\lambda _1}.$$ The ration of $$\frac{{{\lambda _2}}}{{{\lambda _1}}}$$ is proportional to