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 9.5×10 −12 g, if it had absorbed all energy of photon, is nearly:___________.
A. 9x10-3ms-1
B. 10 8ms-1
C. 10-10 ms-1
D. 10-13ms-1

Answer 1

Answer: 9x10-3ms-1 -- A

Explanation:

Given wavelength λ = 505nm

1nm= 10^9m

505nm = 5.05 x10 ^-7m

and speed of light, c  is 3.8 x 10^ 8

frequency = ?

Using  frequency = speed of light / wavelength

f = c/λ

Frequency , f= 3.8 x10^8m/s/ 5.05 x10 ^-7m

=5.94 x 10 ^14 s⁻1

Also Energy = hv

where h =Planck constant  = 6.626 x10 ^ -34 J.s

v= frequency =5.94 x 10 ^14 s⁻1

 Energy = 6.636 x10 ^ -34 J.s x5.94 x 10 ^14 s⁻1

= 3.935 x 10 ^-19J

Given

9.5×10 −12 g as the mass of the bacterium,

changing to kg

1000g= 1kg

9.5×10 −12 g = 9.5×10 −15kg

to find the velocity

Energy = 1/2mv² = E=1/2mv²

v=$\sqrt{2 xE/m}$  =$\sqrt{2 x 3.935 x 10^ -19 / 9.5 x 10^-15}$

v =0.009099=   9x10-3ms-1