Answer :
The kinetic energies and speeds of the two helium atoms are 92.2 keV and [tex]1.49*10^6 m/s[/tex]
Further explanation
An atom a fundamental piece of matter. It is made up of three tiny kinds of particles called subatomic particles such as protons, neutrons, and electron.
Beryllium is a steel-gray metal that is brittle at room temperature.
The kinetic energy of an object is the energy that possesses due to its motion.
A helium atom is an atom of the chemical element helium. Helium is composed of two electrons bound by the electromagnetic force to a nucleus containing two protons along with one or two neutrons depending on the isotope and held together by the strong force.
Let the two helium atom move in opposite direction along the x axis speed [tex]V_1[/tex] and [tex]V_2[/tex]. Convention of momentum along with the [tex]x[/tex] direction. ([tex]P_x, initial = P_x, final[/tex]) given
[tex]0=m_1V_1-m_2V_2 on V_1=V_2[/tex]
The energy is in the form of the total kinetic energy of the two helium atoms
[tex]H_1+H_2=92.2 keV[/tex]
Because [tex]V_1=V_2[/tex], it follows that [tex]H_1=H_2=46.1 keV[/tex] therefore
[tex]v = \frac{2*H_1}{m_1} = \sqrt{\frac{2*(46.1*10^3eV)(1.602*10^{-19} J/eV)}{(4.004)*(1.6605*10^{-27}kg/m)} } = 1.49*10^6 m/s[/tex]
[tex]V_2=V_1=1.49*10^6 m/s[/tex]
Learn more
- Learn more about beryllium https://brainly.com/question/1554284
- Learn more about helium https://brainly.com/question/2882934
Learn more
about energy https://brainly.com/question/9736685
Answer details
Grade: 9
Subject: chemistry
Chapter: atom
Keywords: beryllium, helium, energy, the kinetic energies, speeds
Final answer:
The kinetic energies of the two helium atoms each will be 46.1 keV. To get their speeds, the kinetic energy must be converted to joules and then plugged into the kinetic energy formula, considering that the atoms will have equal momentum but opposite directions due to conservation laws.
Explanation:
The question asks about the kinetics of a nuclear reaction where a beryllium atom splits into two helium atoms, releasing energy in the process. Since the initial beryllium atom is at rest, the conservation of momentum tells us that the two helium atoms will move off in opposite directions with equal momentum but with their kinetic energies distributed according to the released energy.
Given that the mass of the beryllium atom (m = 8.00 u) is twice the mass of a helium atom (m = 4.00 u), and the total energy released from the split is 92.2 keV, we can find the kinetic energy of each helium atom by dividing the total energy by two, due to the conservation of energy. Each helium nucleus will thus get 46.1 keV of kinetic energy, as they share the energy equally.
The calculation of the speeds of the helium atoms will involve converting the kinetic energies from kilo-electron volts to joules and then applying the kinetic energy formula KE = (1/2)mv^2, where m is the mass of the helium atom and v is its speed. To get m in the correct units, we should convert it from atomic mass units (u) to kilograms.
