Light of wavelength l from a small $$0.5$$ mW $$He-Ne$$ laser source, used in the school laboratory, shines from a spacecraft of mass $$1000$$ kg. Estimate the time needed for the spacecraft to reach a velocity of $$1.0$$ $$kms-1$$ from rest. The momentum p of a photon of wavelength l is given by p $$=$$ $$h/l$$, where h is Planck's constant

Question

Light of wavelength l from a small $$0.5$$ mW  $$He-Ne$$ laser source, used in the school laboratory, shines from a spacecraft of mass $$1000$$ kg. Estimate the time needed for the spacecraft to reach a velocity of $$1.0$$ $$kms-1$$ from rest. The momentum p of a photon of wavelength l is given by p $$=$$ $$h/l$$, where h is Planck's constant

Infinity Learn · Accepted Answer

Photons have momentum (P=h$$λ$$) which they carry away, the spacecraft will acquire momentum in the opposite direction according to law of conservation of momentum. No. of photons per second from laser $$=n$$. Then, from energy consideration is $$0.5$$×$$10-3=nh(c$$λ$$)$$      $$n=(0.5$$×$$10-3)$$λ(ch)Rate$$ of change of momentum of $$spacecraftnp=nh$$λ$$=(0.5$$×$$10-3)λ$$ch(h$$λ$$)=0.5$$×$$10-3cFrom$$ Newton's second law,nhλ$$=ma$$⇒$$1000a=0.5$$×$$10-33.00$$×$$108=16$$×$$10-11$$⇒$$v=at$$

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