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Which of the following forms of oxygen can exist freely in nature? A O, B O2, C O3

Physics

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Answer

b

0.9 m\text{0.9 m}

Step-by-step solution

3 steps

Part a· 1 step

OBJECTIVES

  1. The form of oxygen that cannot exist freely in nature is atomic oxygen.

    • A. O
  2. Ions are not fundamental particles of an atom; they are atoms that have gained or lost electrons.

    • B. Ions
  3. Crystalline compounds have a regular, ordered structure, which results in a specific temperature at which all bonds break simultaneously.

    • True
  4. The regular arrangement of atoms in a crystal is known as a crystal lattice.

    • C. Lattice
  5. Step 1: Identify the given values and the formula for Hooke's Law. Given force F=20 NF = 20\, \text{N} and extension x=2 mx = 2\, \text{m}. Hooke's Law states F=kxF = kx, where kk is the spring constant.

  1. Calculate the spring constant kk.

    $$
    k = \frac{F}{x} = \frac{20\, \text{N}}{2\, \text{m}} = 10\, \text{N/m}
    $$
    *   **A. 10 N/m**
    

Part b

0.9 m\text{0.9 m}

THEORY

  1. An atom consists of a central, dense nucleus containing positively charged protons and neutral neutrons. Negatively charged electrons orbit the nucleus in specific energy levels or shells. The number of protons determines the element.

  2. • Cohesion is the attractive force between molecules of the same substance. For example, water molecules are cohesive, causing surface tension.

    • Adhesion is the attractive force between molecules of different substances. For example, water adheres to glass, causing it to climb up a narrow tube (capillary action).
  3. Young's Modulus (or modulus of elasticity) is a measure of the stiffness of an elastic material. It is defined as the ratio of tensile stress to tensile strain within the elastic limit of the material.

    E=Tensile StressTensile Strain=F/AΔL/L0E = \frac{\text{Tensile Stress}}{\text{Tensile Strain}} = \frac{F/A}{\Delta L/L_0}

    where FF is the applied force, AA is the cross-sectional area, ΔL\Delta L is the extension, and L0L_0 is the original length.

  4. Step 1: Calculate the spring constant (kk) using the initial force and extension. Given initial force F1=5 NF_1 = 5\, \text{N} and initial extension x1=0.1 mx_1 = 0.1\, \text{m}. Using Hooke's Law, F1=kx1F_1 = kx_1:

    k=F1x1=5 N0.1 m=50 N/mk = \frac{F_1}{x_1} = \frac{5\, \text{N}}{0.1\, \text{m}} = 50\, \text{N/m}
  1. Calculate the new extension (x2x_2) when the applied force is 20 N20\, \text{N}.

    Given new force $F_2 = 20\, \text{N}$.  
    Using Hooke's Law, $F_2 = kx_2$:
    $$
    x_2 = \frac{F_2}{k} = \frac{20\, \text{N}}{50\, \text{N/m}} = 0.4\, \text{m}
    $$
    
  2. Calculate the total length of the spring.

    The natural length of the spring $L_0 = 0.5\, \text{m}$.  
    The new total length $L_2 = L_0 + x_2$:
    $$
    L_2 = 0.5\, \text{m} + 0.4\, \text{m} = 0.9\, \text{m}
    $$
    The length of the spring when the applied force is $20\, \text{N}$ will be $\boxed{\text{0.9 m}}$.
    
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