Question

В ускорителе заряженных частиц пучок протонов, движущихся со скоростью V= 0,2*10^8 м/с, образует ток I =1 мА. Диаметр пучка d = 2 мм. Найдите концентрацию n протонов в пучке. Сколько протонов попа- дает в мишень за время T=1 ч? Протон – носитель элементарного заряда

Answer 1

V=0.2*10^8 м/с    I=10^-3 A    q=1.6*10^-19 Кл    t=3600 c    d=2*10^-3 м    n=?  N=?
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I=q*n*S*v
S=π*d²/4
n=4*I/(q*π*d²*v)=4*10^-3/(1.6*10^-19*3.14*4*10^-6*0.2*10^8)≈10^14 [1/м3]
N=n*V=n*S*L
L=v*t
N=n*π*d²*v*t/4=10^14*3.14*4*10^-6*0.2*10^8*3600/4≈2.26*10^19 шт
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Answer 2

Calculation of Proton Concentration in the Beam

To find the concentration of protons in the beam, we can use the formula:

n = I / (q * A * V)

Where: - n is the concentration of protons in the beam, - I is the current of the beam (given as 1 mA), - q is the elementary charge (charge of a proton), - A is the cross-sectional area of the beam, - V is the velocity of the protons in the beam.

Given: - I = 1 mA (milliampere), - V = 0.2 * 10^8 m/s (meters per second), - d = 2 mm (diameter of the beam).

To calculate the cross-sectional area A, we can use the formula:

A = π * (d/2)^2

Substituting the given values into the formulas, we can calculate the concentration of protons in the beam.

Let's calculate it step by step.

1. Calculate the cross-sectional area A: - d = 2 mm = 0.002 m - A = π * (0.002/2)^2 = π * 0.001^2 = 3.14159 * 0.000001 = 0.00000314159 m^2

2. Calculate the concentration n: - I = 1 mA = 0.001 A - q = elementary charge = 1.602176634 * 10^-19 C - V = 0.2 * 10^8 m/s - n = 0.001 / (1.602176634 * 10^-19 * 0.00000314159 * 0.2 * 10^8) = 0.001 / (5.02654825 * 10^-26) = 1.989 * 10^22 protons/m^3

Therefore, the concentration of protons in the beam is approximately 1.989 * 10^22 protons/m^3.

Number of Protons Hitting the Target in a Given Time

To calculate the number of protons hitting the target in a given time, we can use the formula:

N = n * A * V * T

Where: - N is the number of protons hitting the target, - n is the concentration of protons in the beam (calculated earlier), - A is the cross-sectional area of the beam (calculated earlier), - V is the velocity of the protons in the beam, - T is the time.

Given: - n = 1.989 * 10^22 protons/m^3 (concentration of protons in the beam), - A = 0.00000314159 m^2 (cross-sectional area of the beam), - V = 0.2 * 10^8 m/s (velocity of the protons in the beam), - T = 1 hour = 3600 seconds.

Let's calculate it step by step.

1. Calculate the number of protons hitting the target N: - n = 1.989 * 10^22 protons/m^3 - A = 0.00000314159 m^2 - V = 0.2 * 10^8 m/s - T = 3600 seconds - N = 1.989 * 10^22 * 0.00000314159 * 0.2 * 10^8 * 3600 = 4.523 * 10^16 protons

Therefore, the number of protons hitting the target in 1 hour is approximately 4.523 * 10^16 protons.

Please note that the calculations provided are based on the given information and assumptions.