Respuesta :
Answer:
a. Radius of the proton (r) = 12.85m
b. Velocity of the proton = 24.62 × 10⁶ m/s
c. Periodic Time (T) = 3.22 × 10⁻⁶ s
Explanation:
The motion of a proton can be described quantitatively and qualitatively by finding the velocity of the proton, the periodic time and radius of the proton.
The first step is to find the Radius of the circular path.
We would derive this formula for Force
Force = mass × acceleration
Where acceleration = (velocity)²/ radius
Therefore
Force of a proton = Force of an electron
(mass of a proton × (velocity)²)/radius of a proton = (mass of a electron × (velocity)²)/radius of a electron
Radius of a proton = (mass of a proton × radius of an electron) ÷ mass of and electron
Mass of a proton = 1.67 × 10⁻²⁷kg
Mass of an electron = 9.1 × 10⁻³¹kg
Radius of an electron = 7.0mm = 7.0 × 10m
Radius of a proton = ( 1.67 × 10⁻²⁷kg× 7.0 × 10⁻³m) ÷ 9.1 × 10⁻³¹kg
Radius of a proton = ( 1.67 × 10⁻²⁷kg × 7.0 × 10⁻³m) ÷ 9.1 × 10⁻³¹kg
Radius of a proton = 12.85m
b. Velocity of a proton =
v = (B × r × q) ÷ m
Where B = Magnetic Flux = 0.020T
r = radius of a proton = 12.85m
q = charge of a proton = 1.602 × 10⁻¹⁹ coulombs
m = mass of a proton = 1.67 × 10⁻²⁷kg
Velocity of a proton = ( 0.020T × 12.85m × 1.602 × 10⁻¹⁹c ) ÷ 1.67 × 10⁻²⁷kg
Velocity of a proton = 24.62 × 10⁶ m/s
c. Periodic Time(T) = (2πr) ÷ v
where r = radius of a proton = 12.85m
v = velocity of a proton = 24.62 × 10⁶ m/s
T = (2 × π × 12.85m) ÷ 24.62 × 10⁶ m/s
= 3.22 × 10⁻⁶ s
a. Radius of the proton (r) = 12.85m
b. Velocity of the proton = 24.62 × 10⁶ m/s
c. Periodic Time (T) = 3.22 × 10⁻⁶ s
Calculation for radius:
As we know, Force = mass × acceleration
where; Acceleration = (velocity)²/ radius
Thus,
Force of a proton = Force of an electron
(mass of a proton × (velocity)²)/radius of a proton = (mass of a electron × (velocity)²)/radius of a electron
Radius of a proton = (mass of a proton × radius of an electron) ÷ mass of and electron
Mass of a proton = 1.67 × 10⁻²⁷kg
Mass of an electron = 9.1 × 10⁻³¹kg
Radius of an electron = 7.0mm = 7.0 × 10m
Radius of a proton = ( 1.67 × 10⁻²⁷kg× 7.0 × 10⁻³m) ÷ 9.1 × 10⁻³¹kg
Radius of a proton = ( 1.67 × 10⁻²⁷kg × 7.0 × 10⁻³m) ÷ 9.1 × 10⁻³¹kg
Radius of a proton = 12.85m
Calculation for velocity:
v = (B × r × q) ÷ m
where,
B = Magnetic Flux = 0.020T
r = radius of a proton = 12.85m
q = charge of a proton = 1.602 × 10⁻¹⁹ coulombs
m = mass of a proton = 1.67 × 10⁻²⁷kg
Velocity of a proton = ( 0.020T × 12.85m × 1.602 × 10⁻¹⁹c ) ÷ 1.67 × 10⁻²⁷kg
Velocity of a proton = 24.62 × 10⁶ m/s
Calculation for time period:
Periodic Time(T) = (2πr) ÷ v
where,
r = radius of a proton = 12.85m
v = velocity of a proton = 24.62 × 10⁶ m/s
T = (2 × π × 12.85m) ÷ 24.62 × 10⁶ m/s
Time period (T) = 3.22 × 10⁻⁶ s
Find more information about Acceleration here:
brainly.com/question/22048837
