Question

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 y if released into free space and assumed to live

Answer 1

Answer:

  a = Np/10 yrs×[3.50^7 yrs /sec]

Explanation:

The energy of the single photon of frequency f or wave length λ  is given as

   E = hc / λ

since the glow warm emits energy 0.1 J/sec

that is  the number of photons n emitted by the photon per sec will be

n = 0.1 W / E

Thus, the number of photons emitted in 10 years

 N = n×3.15×10^7 sec/yr ×10 yr

Now, momentum associated with each photon

p= h / λ

and, momentum associated with N photon particles

P= N(h/λ)    

hence the change in the momentum of the glow is = Np in 10 years

Therefore, acceleration of the glow

                a = Np/10 yrs×[3.50^7 yrs /sec]

Answer 2

Answer:

The speed is 21.06 m/s.

Explanation:

Given that,

mass of glow worm = 5.0 g

Wavelength = 650 nm

Power = 0.10 W

Time = 10 years

The total energy emitted in a period $\tau$ is $P\tau$

The energy of single photon of frequency or wavelength is

$E=\dfrac{hc}{\lambda}$

The total number of photons emitted in a interval $\tau$ is then the total energy divided by the energy per photon.

$N=\dfrac{P\tau}{E}$

$N=\dfrac{P\tau\times\lambda}{hc}$

$N=\dfrac{P\tau\times\lambda}{hc}$

We need to calculate the speed

Using de Broglie's relation applies to each photon and thus the total momentum imparted to the glow-worm

$p=\dfrac{Nh}{\lambda}$

$p=\dfrac{\dfrac{P\tau\times\lambda}{hc}\times h}{\lambda}$

$p=\dfrac{P\tau}{c}$

$v=\dfrac{P\tau}{mc}$

Put the value into the formula

$v=\dfrac{0.10\times3.16\times10^{8}}{5.0\times10^{-3}\times3\times10^{8}}$

$v=21.06\ m/s$

Hence, The speed is 21.06 m/s.