   Chapter 34, Problem 24PE

Chapter
Section
Textbook Problem

Supermassive black holes are thought to exist at the center of many galaxies.(a) What is the radius of such an object if it has a mass of 109 Suns?(b) What is this radius in light years?

To determine

(a)

The radius of the object having a mass of 109 times the mass of the sun.

Explanation

Given:

Mass of Sun, ms=1.989×1030kg

Speed of light, c=3×108m/s

Gravitational constant, G=6.67×1011N-m2/kg2

Formula used:

Formula to calculate the Schwarzschild radius of a black hole is,

Rsc=2Gmc2 ...... (I)

Where,

• Rsc is Schwarzschild radius.
• G is gravitational constant.
• m is mass of the object.
• c is speed of light.

Calculation:

Super massive black holes are thought to exist at the center of any galaxy and these are the largest type of the black holes. In order to determine the radius of the object, determine the Schwarzschild radius.

Since, the mass of the object is 109 times the mass of the sun.

Calculate the mass of the black hole.

m=109×ms

Substitute 1.989×1030kg for me in the above expression.

m=109×1.989×1030kg=1.989×1039kg

Substitute 1

To determine

(b)

The radius of the object in terms of light years.

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