Question

The human eye is most sensitive to green light of wavelength 505 nm. Experiments have found that when people are kept in a dark room until their eyes adapt to the darkness, a single photon of green light will trigger receptor cells in the rods of the retina. The velocity of typical bacterium of mass $9.5\times {10}^{-12}$g, if it had absorbed all energy of photon, is nearly:

• A. $9\times {10}^{-3}m{s}^{-1}$
• B. ${10}^{8}m{s}^{-1}$
• C. ${10}^{-10}m{s}^{-1}$
• D. ${10}^{-13}m{s}^{-1}$

Answer 1

The correct option is A $9\times {10}^{-3}m{s}^{-1}$

If the bacterium absorbs photon

$\frac{1}{2}m{v}^2=\frac{hc}{\lambda }\lambda =505\times {10}^{-9}mm=9.5\times {10}^{-3}\times {10}^{-12}kgv=\sqrt{\frac{hc}{m\lambda }}=\sqrt{\frac{2\times 6.6\times {10}^{-34}\times 3\times {10}^8}{9.5\times {10}^{-15}\times 505\times {10}^{-9}}}=9\times {10}^{-3}m/sec$