If a sample of calcium chloride is introduced into a nonluminous flame, the color of the flame turns to orange (“flame test”). The light is emitted because calcium atoms become excited; their return to the ground state results in light emission. (c) Calculate the energy gap between the excited and ground states for the calcium atom.

Verified step by step guidance

Understand the concept of a flame test: When calcium chloride is introduced into a flame, calcium atoms absorb energy and become excited. As they return to their ground state, they emit light of a characteristic color, which is orange for calcium.

Identify the wavelength of the emitted light: The orange color corresponds to a specific wavelength in the visible spectrum. You can use reference materials or a spectrometer to find the approximate wavelength of the orange light emitted by calcium.

Use the formula for energy of a photon: The energy of a photon can be calculated using the formula \( E = \frac{hc}{\lambda} \), where \( E \) is the energy, \( h \) is Planck's constant \( (6.626 \times 10^{-34} \text{ J s}) \), \( c \) is the speed of light \( (3.00 \times 10^8 \text{ m/s}) \), and \( \lambda \) is the wavelength of the emitted light.

Convert the wavelength to meters: If the wavelength is given in nanometers (nm), convert it to meters by multiplying by \( 10^{-9} \). This ensures that all units are consistent when using the formula.

Substitute the values into the formula: Plug the values for \( h \), \( c \), and \( \lambda \) into the formula to calculate the energy gap between the excited and ground states for the calcium atom.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Energy Levels in Atoms

Atoms have quantized energy levels, meaning electrons can only exist in specific energy states. When an electron absorbs energy, it can move from a lower energy level (ground state) to a higher one (excited state). The difference in energy between these levels is what determines the wavelength and color of light emitted when the electron returns to the ground state.

Flame Test

The flame test is a qualitative analysis technique used to identify the presence of certain metal ions based on the color of the flame produced when the sample is heated. Different metals emit characteristic colors due to the excitation of their electrons, which release energy in the form of light as they return to their ground state. For calcium, this results in an orange flame.

Energy Calculation

The energy gap between the excited and ground states can be calculated using the formula E = hν, where E is the energy, h is Planck's constant, and ν (nu) is the frequency of the emitted light. Alternatively, the energy can also be expressed in terms of wavelength using E = hc/λ, where c is the speed of light and λ (lambda) is the wavelength. This calculation is essential for quantifying the energy transitions in atomic systems.

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If a sample of calcium chloride is introduced into a nonluminous flame, the color of the flame turns to orange ('flame test'). The light is emitted because calcium atoms become excited; their return to the ground state results in light emission. (b) What is the energy of 1.00 mol of these photons (a mole of photons is called an Einstein)?

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