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Inorganic chemistry Assistance Lecturer Amjad Ahmed Jumaa Calculating the number of atoms in a given amount of a compound. Calculating the Frequency and Wavelength of an Electromagnetic Wave,. Calculating the energy of a photon. 1
Calculating the number of atoms in a given amount of a compound: convert from grams of compound to moles of a particular atom to number of atoms. Let's try an example. Example: How many carbon atoms are present in (50.3 g) of (C 2 H 6 ). Solution: We started this problem in the above example, when we calculated the moles of ethane in (50.3 g ethane). To continuo, we need two additional conversion factors. One should represent the mole ratio between moles of( C ) atoms and moles of ethane molecules. The other conversion factor needed is Avogadro's number.
Step(1): the two conversion factors needed are: You should come up with the following strategy: Grams of C 2 H 6 → moles of C 2 H 6 → moles of C → atoms of C. Step (2): = 2.01 x C atom.
Calculating the frequency and wavelength of an electromagnetic wave: All types of electromagnetic radiation move through a vacuum at a speed of about (3.00 x 10 8 m/s), which is called the speed of light( c), speed is an important property of a wave traveling through space and is equal to the product of the wavelength and the frequency of the wave. For electromagnetic waves : c = λv …………………….. (1). Equation (1) can be rearranged as necessary to solve for either the wavelength (λ) or the frequency (v). Example: A certain (AM) radio station broadcasts at a frequency (6.00 x 10 2 kHz). What is the wavelength of these radio wave in meters.
Solution: Step(1): solve the equation (1) algebraically for the wavelength (λ). c = λv Step (2): since the speed of light has units of (m/s). We must convert the frequency from units of (kHz) to (Hz)(s -1 ) x 10 2 kHz x = 6.00 x 10 5 Hz = 6.00 x 10 5 s -1. Step (3): calculate the value of (λ) by substituting the known quantities into equation (2). λ = = 5.00 x 10 2 m. ……………………(2)
Example (2): What is the frequency of light that has a wavelength of (665) (nm). Solution: Step (1): solve equation (1) algebraically for the frequency (v). c = λv …………………..(3) Step (2): since the speed of light has units of (m/s). we must convert the wavelength from units of (nm) to (m). 665 nm x = 6.65 x m. Step (3): calculate the value of (v) by substituting the known quantities into equation (3).
= 4.51 x s -1 = 4.51 x Hz Calculating the energy of a photon: atoms and molecules could emit( or absorb) energy only in discrete quantities. Planck gave the name (quantum) to the smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation. The energy (E) of a single quantum of energy is given by: E = hν …………………..(4) h is Planck's constant = 6.63 x J.s ν is the frequency of radiation. v =
Example: The yellow light given off by a sodium vapor lamp has a wavelength of (589nm), what is the energy of a single photon of this radiation. Solution: Step (1): you are given wavelength in this problem. Equation (4) shows the relationship between energy and frequency. However, there is a relationship between frequency and wavelength (see equation 3). Substituting for the frequency in equation (4), we have: ………5 Step (2): since the speed of light is in units of (m/s), we must convert the wavelength from units of (nm) to (m).
x = 5.89 x m. Step (3): Calculate the value of (E) by substituting the known quantities into equation (5). E = = 3.38 x J.