Question

A modest supernova (the explosion of a massive star at the end of its life cycle) releases 1.5 * 1044 J of energy in a few seconds. This is enough to outshine the entire galaxy in which it occurs. Suppose a star with the mass of our sun collides with an antimatter star of equal mass, causing complete annihilation. What is the ratio of the energy released in this star-antistar collision to the energy released in the supernova?

Short answer

The ratio of the energy released in this star-antistar collision to the energy released in the supernova 2400.

Step-by-step solution

Given information

We have given that, a modest supernova (the explosion of a massive star at the end of its life cycle) releases 1.5 * 1044 J of energy in a few seconds. This is enough to outshine the entire galaxy in which it occurs. Suppose a star with the mass of our sun collides with an antimatter star of equal mass, causing complete annihilation.

Step 1.

All the mass will be converted in energy in the collision.

We can write it as $E=m{c}^2$.

Here, E = energy

m = mass

c = speed of light

Step 2.

We have given that mass of star and anti star is equal to the mass of Sun.

So, the energy given in star and anti star collision is :

$E=2m_{sun}{c}^2$

here, E = energy

$m_{sun}$= mass of sun

c = speed of light

Substituting the values in energy formula :

$E=2\times (1.99\times {10}^{30}Kg)\times {(3\times {10}^{8}m/s)}^2$

$E=3.58\times {10}^{47}J$

The ratio of the energy released in this star-antistar collision to the energy released in the supernova :

$\frac{3.58\times {10}^{47}J}{1.5\times {10}^{44}J}=2400$