Respuesta :
Answer:
a) x_{cm} = m₂/ (m₁ + m₂) d , b) x_{cm} = 52.97 pm
Explanation:
The expression for the center of mass is
[tex]x_{cm}[/tex] = 1 / M ∑ [tex]x_{i}[/tex] [tex]m_{i}[/tex]
Where M is the total masses, mI and xi are the mass and position of each element of the system.
Let's fix our reference system on the oxygen atom and the molecule aligned on the x-axis, let's use index 1 for oxygen and index 2 for carbon
x_{cm} = 1 / (m₁ + m₂) (0+ m₂ x₂)
Let's reduce the magnitudes to the SI system
m₁ = 17 u = 17 1,661 10⁻²⁷ kg = 28,237 10⁻²⁷ kg
m₂ = 12 u = 12 1,661 10⁻²⁷ kg = 19,932 10⁻²⁷ kg
d = 128 pm = 128 10⁻¹² m
The equation for the center of mass is
x_{cm} = m₂/ (m₁ + m₂) d
b) let's calculate the value
x_{cm} = 19.932 10⁻²⁷ /(19.932+ 28.237) 10⁻²⁷ 128 10-12
x_{cm} = 52.97 10⁻¹² m
x_{cm} = 52.97 pm
(a) The expression for the center mass of these two atoms relative to oxygen atom is [tex]X_{cm} = \frac{m_1 d_0 \ +\ m_2d}{m_1 + m_2}[/tex]
(b) The numeric value for the center of mass of carbon monoxide is 53 pm.
The given parameters;
- mass of the carbon atom = 12u
- mass of the oxygen atom, = 17 u
- distance between the atoms, = 128 pm
The center mass of these two atoms relative to oxygen atom is calculated as follows;
[tex]X_{cm} = \frac{m_1 d_0 \ +\ m_2d}{m_1 + m_2}[/tex]
where;
- [tex]d_0[/tex] is distance of the atom in the fixed reference point (oxygen atom)
(b)
The numeric value for the center of mass of carbon monoxide in units of pm is calculated as follows;
[tex]X_{cm} = \frac{17u(0) \ +\ 12u(128 \ pm)}{(12u + 17u)}\\\\X_{cm} = \frac{(12 \times 128u) \ pm}{29u} \\\\X_{cm} = 53 \ pm[/tex]
Learn more here:https://brainly.com/question/13981379
