Question

Рассчитайте, во сколько раз уменьшится скорость атома гелия после центрального упругого столкновения с неподвижным атомом водорода, масса которого в 4 раза меньше массы атома гелия. Должен получиться ответ: в 1,67 раза Нужно решение с объяснением.

Answer 1

Составим систему из двух уравнений:

1. Закон сохранения импульса:

m1 * V01 = m1*V1 + m2 * V2

2. Закон сохранения энергии:

m1V01^2/2 = m1V1^2/2 * m1V2^2/2

или же:

m1 * V01^2 = m1V1^2 * m1V2^2

Максимально упрощаем нашу систему для деления, приведя подобные и вынеся общие множители:

m1*V0 - m1*V1 = m2 * V2

m1*V0^2 - m1*V1^2 = m2 * V2^2

m1(V0 - V1) = m2 * V2

m1(V0^2 - V1^2) = m2 * V2

Делим и получаем:

V0 + V1 = V2

или же распишу более подробно:

m1 * V0 = m1 * V1 + m2(V0 + V1) (это закон сохранения импульса с заменой V2 на V1 + V0)

m1 * V0 = m1 * V1 + m2 * V0 + m2 * V1

(m1 - m2) * V0 = (m1+m2) * V1

Отсюда:

V1 = m1 - m2 *V0/m1 + m2

Теперь введем замену, обращая внимания на то, что по условию масса H < He в 4 раза.

t = m1/m2 = 4

n = V0/V1 = m1 + m2/m1- m2 = m1/m2 + 1/m1/m2  - 1= t +1/t-1 = 5/3 = 1.67

Answer 2

Calculation of the Change in Velocity of a Helium Atom after Collision with a Hydrogen Atom

To calculate the change in velocity of a helium atom after a central elastic collision with a stationary hydrogen atom, we can use the principles of conservation of momentum and kinetic energy.

Let's denote the mass of the helium atom as m_helium and the mass of the hydrogen atom as m_hydrogen. Given that the mass of the hydrogen atom is 4 times smaller than the mass of the helium atom, we can express this relationship as:

m_hydrogen = (1/4) * m_helium.

In an elastic collision, both momentum and kinetic energy are conserved. Therefore, we can write the following equations:

1. Conservation of momentum: m_helium * v1_helium + m_hydrogen * v1_hydrogen = m_helium * v2_helium + m_hydrogen * v2_hydrogen,

where v1_helium and v1_hydrogen are the initial velocities of the helium and hydrogen atoms, respectively, and v2_helium and v2_hydrogen are their final velocities.

2. Conservation of kinetic energy: (1/2) * m_helium * v1_helium^2 + (1/2) * m_hydrogen * v1_hydrogen^2 = (1/2) * m_helium * v2_helium^2 + (1/2) * m_hydrogen * v2_hydrogen^2.

We are interested in calculating the change in velocity of the helium atom, which can be expressed as:

change in velocity = v2_helium - v1_helium.

To solve these equations, we need additional information such as the initial velocities of the atoms. Unfortunately, the given information does not provide the initial velocities. Therefore, without this information, we cannot calculate the exact change in velocity of the helium atom after the collision.

However, we can make some general observations based on the given information. Since the mass of the hydrogen atom is smaller than the mass of the helium atom, we can expect that the helium atom will experience a smaller change in velocity compared to the hydrogen atom after the collision. This is because the lighter hydrogen atom will be affected more by the collision due to its smaller mass.

Therefore, it is reasonable to conclude that the change in velocity of the helium atom will be less than the change in velocity of the hydrogen atom. However, without the specific initial velocities, we cannot determine the exact ratio of the change in velocity between the two atoms.

In summary, without the specific initial velocities, we cannot calculate the exact change in velocity of the helium atom after the collision. However, based on the given information, we can expect that the change in velocity of the helium atom will be smaller than the change in velocity of the hydrogen atom.