Question

This question relates to the practicality of searching for intelligent life in other solar systems by detecting their radio broadcasts (or aliens find us from ours). The closest stars are 4 light years away from us. How far away must you be from a 781 kHz radio station with power 50.0 kW for there to be only one photon per second per square meter? Assume that the photons spread out spherically. The area of a sphere is 4????????2.

Answer 1

Answer:

$2.77287\times 10^{15}\ m$

Explanation:

P = Power = 50 kW

n = Number of photons per second

h = Planck's constant = $6.626\times 10^{-34}\ m^2kg/s$

$\nu$ = Frequency = 781 kHz

r = Distance at which the photon intensity is i = 1 photon/m²

Power is given by

$P=nh\nu\\\Rightarrow n=\dfrac{P}{h\nu}\\\Rightarrow n=\dfrac{50000}{6.626\times 10^{-34}\times 781000}\\\Rightarrow n=9.66201\times 10^{31}\ photons/s$

Photon intensity is given by

$i=\dfrac{n}{4\pi r^2}\\\Rightarrow 1=\dfrac{9.66201\times 10^{31}}{4\pi r^2}\\\Rightarrow r=\sqrt{\dfrac{9.66201\times 10^{31}}{4\pi}}\\\Rightarrow r=2.77287\times 10^{15}\ m$

The distance is $2.77287\times 10^{15}\ m$

Answer 2

You must stay at a distance of $2.77287*10^1^5m$

How can we arrive at this result?

• First, we have to find the number of protons per second. This will be done using the equation: $n= \frac{P}{h*v}$

In this equation, the "h" represents Planck's constant and will take on the value of  $6.626*10^-^3^4m^2\frac{Kg}{s}$

The "r" will be equal to 1 photon/m² and the "P' will be equal to 50 kW.

Therefore, we will solve the equation as follows:

$n= \frac{50000}{(6.626*10^-^3^4*781000)}= 9.66201*10^3^1 \frac{protons}{s}$

• From this value, we can calculate the appropriate distance for you to position yourself. For this, we will use the equation:

$r^2=\frac{n}{4*\pi} \\r= \sqrt{\frac{9.6621*10^3^1}{4*\pi } } = 2.77287*10^1^5m$

More information about protons is in the link:

https://brainly.com/question/1013246