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

a = Np/10 yrs×[3.50^7 yrs /sec]

Step-by-step 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

The speed is 21.06 m/s.

Step-by-step 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=(hc)/(\lambda)`

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

`N=(P\tau)/(E)`

`N=(P\tau*\lambda)/(hc)`

`N=(P\tau*\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=(Nh)/(\lambda)`

`p=((P\tau*\lambda)/(hc)* h)/(\lambda)`

`p=(P\tau)/(c)`

`v=(P\tau)/(mc)`

Put the value into the formula

`v=(0.10*3.16*10^(8))/(5.0*10^(-3)*3*10^(8))`

`v=21.06\ m/s`

Hence, The speed is 21.06 m/s.