How can one use the formula to calculate the lifetime of a black hole with the mass of the sun?

Answer 1

Well sweetheart, calculating the lifetime of a black hole with the mass of the sun involves a little thing called Hawking radiation. You use the formula Time = 5120 x pi x (G^2 x M^3) / (h x c^4) to crunch those numbers. So grab a calculator, put on your thinking cap, and dive into the fascinating world of astrophysics.

Answer 2

To calculate the lifetime of a black hole with the mass of the sun, you can use the formula for Hawking radiation. This formula relates the mass of the black hole to the rate at which it loses mass over time. By plugging in the mass of the sun into the formula, you can determine how long it would take for the black hole to completely evaporate.

Answer 3

Ah, what a fascinating question, my friend. Let's paint a picture here. You see, to calculate the lifetime of a black hole with the mass of the sun, one could use the formula based on Hawking radiation. By plugging in the mass of the black hole (equal to the mass of the sun) into the formula, you can find a lovely estimation of its lifetime. Remember, these calculations paint a beautiful portrait of the cosmos for us to admire and ponder.

Answer 4

Oh, dude, calculating the lifetime of a black hole is like trying to figure out how long your roommate's leftovers will last in the fridge - a total mystery. But basically, you can use the formula for Hawking radiation, which depends on the mass of the black hole. So for a black hole the mass of the sun, just plug that number into the formula and voila, you've got your answer, or you know, a rough estimate 'cause those things can be unpredictable, man.

Answer 5

To calculate the lifetime of a black hole with the mass of the sun, we can use the formula for the evaporation time of a black hole due to Hawking radiation. This formula is known as the Hawking radiation formula and is derived from quantum field theory in curved spacetime.

The formula for the evaporation time of a black hole due to Hawking radiation is given by:

[ t = \frac{5120 \pi G^2 M^3}{\hbar c^4} ]

Where:

• ( t ) is the evaporation time of the black hole,
• ( G ) is the gravitational constant (( G \approx 6.67430 \times 10^{-11} , \text{m}^3 , \text{kg}^{-1} , \text{s}^{-2} )),
• ( M ) is the mass of the black hole (mass of the sun is ( M \approx 1.989 \times 10^{30} , \text{kg} )),
• ( \hbar ) is the reduced Planck's constant (( \hbar \approx 1.0545718 \times 10^{-34} , \text{J s} )),
• ( c ) is the speed of light in a vacuum (( c \approx 2.998 \times 10^8 , \text{m/s} )).

Now, plugging in the values for ( G ), ( M ), ( \hbar ), and ( c ), we can calculate the evaporation time of a black hole with the mass of the sun.

[ t = \frac{5120 \pi \times (6.67430 \times 10^{-11} , \text{m}^3 , \text{kg}^{-1} , \text{s}^{-2})^2 \times (1.989 \times 10^{30} , \text{kg})^3}{(1.0545718 \times 10^{-34} , \text{J s}) \times (2.998 \times 10^8 , \text{m/s})^4} ]

Upon calculation, we can determine the evaporation time of a black hole with the mass of the sun.