Question

How long would gamma radiation take to travel from sun to earth, a distance of \[1.5 \times {10^{11}}{\rm{ m}}\]?

Answer 1

Hint: We will use the concept of generation of the electromagnetic spectrum to determine the velocity of gamma radiation. Later, we will also use the expression of speed of gamma radiation, which is given in terms of distance traveled, and time period of gamma radiation.

Complete step by step answer:
Given:
The distance between the sun and earth is equal to \[1.5 \times {10^{11}}{\rm{ m}}\].
We know that gamma radiation is a part of the electromagnetic radiation spectrum obtained when white light is allowed to pass through a diffraction medium.
The speed of light is represented by c and is equal to \[3 \times {10^8}{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {\rm{s}}}} \right.
 } {\rm{s}}}\].
We also know that gamma radiation is obtained from white light; therefore, we can say that gamma radiation's speed is equal to the speed of light.
\[
v = c\\
\Rightarrow v= 3 \times {10^8}{{\rm{m}} {\left/
{\vphantom {{\rm{m}} {\rm{s}}}} \right.
} {\rm{s}}}
\]
The relationship of velocity, distance traveled, and time period of gamma radiation at any time instant t is expressed as:
\[
v = \dfrac{d}{t}\\
\Rightarrow t = \dfrac{d}{v}
\]
Here v is the velocity of gamma radiation, and d is the distance traveled by gamma radiation.
Substitute \[1.5 \times {10^{11}}{\rm{ m}}\] for d and \[3 \times {10^8}{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {\rm{s}}}} \right.
 } {\rm{s}}}\] for v in equation (1) to get the value of time taken by gamma radiation to reach earth starting from the sun.
\[
t = \dfrac{{1.5 \times {{10}^{11}}{\rm{ m}}}}{{3 \times {{10}^8}{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {\rm{s}}}} \right.
 } {\rm{s}}}}}\\
\therefore t = 500{\rm{ s}}
\]

Therefore, the time taken by gamma radiation to travel from the sun to earth is equal to \[500{\rm{ s}}\].

Note: In the solution, we need the velocity of gamma radiation, which is unknown, so do not confuse how to find it as it is equal to the speed of light because gamma radiation is a part of the electromagnetic spectrum of light.