A photon of an X-ray radiation has a wavelength of 5.50 Å. For the radiation, calculate the (a)frequency in Hertz, (b)the energy in Joules, (c) the energy in electron volts (eV) and (d) the energy in kJ/mol.
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To calculate the frequency of the X-ray radiation, you can use the equation:
frequency = speed of light / wavelength
Given that the speed of light is approximately 3.00 x 10^8 m/s (exact value is 299,792,458 m/s), we need to convert the wavelength from Ångstroms to meters.
1 Ångstrom (Å) = 1 x 10^-10 meters
(a) Frequency in Hertz:
Using the conversion, the wavelength in meters is: 5.50 Å * (1 x 10^-10 m/Å) = 5.50 x 10^-10 m
Now, we can calculate the frequency:
frequency = (3.00 x 10^8 m/s) / (5.50 x 10^-10 m) = 5.45 x 10^17 Hz
(b) Energy in Joules:
To calculate the energy of a photon, you can use the equation:
energy = Planck's constant * frequency
The value of Planck's constant is approximately 6.63 x 10^-34 J·s.
energy = (6.63 x 10^-34 J·s) * (5.45 x 10^17 Hz) = 3.61 x 10^-16 J
(c) Energy in electron volts (eV):
To convert energy from Joules to electron volts, you can use the conversion factor:
1 eV = 1.60 x 10^-19 J
energy_eV = (3.61 x 10^-16 J) / (1.60 x 10^-19 J/eV) = 2.26 x 10^3 eV
(d) Energy in kilojoules per mole (kJ/mol):
To convert energy from Joules to kilojoules per mole, you can use Avogadro's constant:
Avogadro's constant = 6.022 x 10^23 mol^-1
energy_kJmol = (3.61 x 10^-16 J) / (1000 J/kJ) * (6.022 x 10^23 mol^-1) = 2.17 x 10^9 kJ/mol
Therefore, the answers for each calculation are:
(a) Frequency: 5.45 x 10^17 Hz
(b) Energy: 3.61 x 10^-16 J
(c) Energy in eV: 2.26 x 10^3 eV
(d) Energy in kJ/mol: 2.17 x 10^9 kJ/mol