Question

Порошина массой 10нг, несущая на себе 20 электронов, прошла в вакууме ускорительную разницу потенциалов 2 МВ. Какую скорость набрала порошина? Какая кинетическая энергия порошины?

Answer 1

Дано:                   Решение:

m = 10 нг              Ek=Eп

N=20                     mv^2/2=eU  => Eк=qu=1.6*10^-19*2*10^6=3.2*10^-12

U= 2 МВ               Нашли кин.энергию, найдем и скорость:

q=e                      v^2=2eU/m => v=√2eU/m

Найти:                v=√6.4*10^-12/10*10^-9 = 0.025

v-?              Ответ: Eк=3.2*10^-12 ; v=0.025

E-?

Answer 2

Calculation of the Speed of the Particle

To calculate the speed of the particle, we can use the equation for the kinetic energy of a particle:

Kinetic Energy (KE) = (1/2) * m * v^2

where KE is the kinetic energy, m is the mass of the particle, and v is the velocity of the particle.

Given that the mass of the particle is 10 ng (nanograms) and it carries 20 electrons, we can assume that the particle is an electron. The mass of an electron is approximately 9.10938356 × 10^-31 kilograms.

Converting the mass of the particle to kilograms: 10 ng = 10 * 10^-12 kg = 1 * 10^-11 kg

Since the particle is accelerated by a potential difference of 2 MV (megavolts), we can use the equation for the potential energy of a charged particle:

Potential Energy (PE) = q * V

where PE is the potential energy, q is the charge of the particle, and V is the potential difference.

The charge of an electron is approximately -1.602176634 × 10^-19 coulombs.

Converting the potential difference to volts: 2 MV = 2 * 10^6 volts

Now, we can equate the potential energy to the kinetic energy to find the velocity of the particle:

PE = KE q * V = (1/2) * m * v^2

Substituting the values: (-1.602176634 × 10^-19 C) * (2 * 10^6 V) = (1/2) * (1 * 10^-11 kg) * v^2

Simplifying the equation: v^2 = (2 * (-1.602176634 × 10^-19 C) * (2 * 10^6 V)) / (1 * 10^-11 kg)

Taking the square root of both sides to find the velocity: **v = sqrt((2 * (-1.602176634 ×