A glow–worm of mass 5.0 g emits red light (650 nm) with a power of 0.10 w. entirely in the backward direction. To what speed will it have accelerated after 10 year if released into free space and assumed to live?
Text Solution
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The total energy emitted in a period τ is p τ . The energy of a photon of 650 nm light is E = 
with λ = 650 nm. The total number of photons emitted in a interval τ is then the total energy divided by the energy per photon.
N = 
= 
DeBroglie’s relation applies to each photon and thus the total momentum imparted to the glow–worm
is p = 
= 
× 
= 
P = 0.10 w = 0.10 J s –1 , τ = 10y, p = mv
Hence the final speed is :
v = 
= 
= 21 ms –1
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