We encounter a large number of waves every day without realizing it. One such source is radio waves. A typical frequency for radio transmission is 680 kHz. How much energy does one mole of radio waves carry? X rays used by doctors to view bones are much more energetic than radio waves. Determine the energy of one mole of X ray photons (3.8 x 1017 Hz).
E for one atom = h*frequency.
Multiply by 6.022E23 to determine E in a mole. Both parts are done the same way
To determine the energy of one mole of radio waves and X-ray photons, we need to use the equations that relate energy to frequency of electromagnetic waves.
The energy of a photon can be calculated using the equation:
E = hf
where E is the energy of the photon, h is the Planck's constant (6.626 x 10^-34 J·s), and f is the frequency of the wave.
To find the energy of one mole of photons, we need to multiply the energy of one photon by Avogadro's number (6.022 x 10^23 mol^-1) since one mole contains Avogadro's number of particles.
Let's first calculate the energy of one mole of radio waves:
Given frequency: f = 680 kHz = 680 x 10^3 Hz
Using the equation E = hf, we can substitute the values:
E = (6.626 x 10^-34 J·s) x (680 x 10^3 Hz)
Calculating this expression, we find:
E = 4.505 x 10^-26 J
Now, to find the energy of one mole of radio waves, we multiply this value by Avogadro's number:
Energy of one mole of radio waves = (4.505 x 10^-26 J) x (6.022 x 10^23 mol^-1)
Calculating this, we get:
Energy of one mole of radio waves = 2.712 x 10^-2 J/mol
Now let's calculate the energy of one mole of X-ray photons:
Given frequency: f = 3.8 x 10^17 Hz
Using the equation E = hf, we substitute the values:
E = (6.626 x 10^-34 J·s) x (3.8 x 10^17 Hz)
Calculating this expression, we find:
E = 2.517 x 10^-15 J
To find the energy of one mole of X-ray photons, we multiply this value by Avogadro's number:
Energy of one mole of X-ray photons = (2.517 x 10^-15 J) x (6.022 x 10^23 mol^-1)
Calculating this, we get:
Energy of one mole of X-ray photons = 1.515 x 10^9 J/mol
Therefore, one mole of radio waves carries approximately 2.712 x 10^-2 J of energy, while one mole of X-ray photons carries approximately 1.515 x 10^9 J of energy.