A synchrotron radiation facility consists of a circular ring that has a 48.0 m radius and creates an electron beam with a current of 497 mA when the electrons have a speed approximately equal to the speed of light. How many electrons pass a given point in the accelerator per hour?
PLEASE SHOW EVERY STEP AND CIRCLE OR SAY WHAT IS THE FINAL ANSWER!!
an Ampere is a Coulomb per second
a Coulomb is the charge on
6.242 x 10¹⁸ electrons
there are 3600 seconds in an hour
.497 * 6.242E18 * 3.6E3 = answer
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To determine the number of electrons that pass a given point in the accelerator per hour, we need to calculate the total charge passing through that point and then convert it to the number of electrons.
First, let's calculate the total charge passing through the given point in one second:
1. Calculate the circumference of the circular ring:
Circumference = 2 * π * radius
= 2 * 3.14 * 48.0 m
= 301.44 m
2. Calculate the distance traveled by electrons in one second:
Distance = speed * time
= 3 x 10^8 m/s * 1 s (since the electron speed is approximately the speed of light)
= 3 x 10^8 m
3. Calculate the current in Coulombs (C) passing through the point per second:
Current = 497 mA = 497 x 10^-3 A
Charge = Current * Time
= 497 x 10^-3 A * 1 s
= 497 x 10^-3 C
Now, let's convert the charge in Coulombs to the number of electrons:
4. Determine the charge of a single electron (e):
The charge of an electron (e) is equal to 1.6 x 10^-19 C.
5. Calculate the number of electrons passing through the point per second:
Number of electrons = Charge / e
= 497 x 10^-3 C / (1.6 x 10^-19 C)
= 3.10625 x 10^16
To find the number of electrons passing the given point in the accelerator per hour, we need to multiply this value by the number of seconds in an hour.
6. Calculate the number of seconds in an hour:
1 hour = 60 minutes
1 minute = 60 seconds
Number of seconds in an hour = 60 min/hour * 60 sec/min = 3600 sec/hour
7. Calculate the number of electrons passing the point per hour:
Number of electrons per hour = Number of electrons * Number of seconds in an hour
= 3.10625 x 10^16 * 3600
= 1.11825 x 10^20
Therefore, approximately 1.11825 x 10^20 electrons pass the given point in the accelerator per hour.