A mixture of argon and mercury vapor used
in advertising signs emits light of wavelength 610 nm.
Calculate the energy change resulting from
the emission of 1.00 mol of photons at this wavelength.
Answer in units of kJ/mol.
Use E=hc/lambda to calculate the energy (in J).
This is the energy of one photon. There are 6.02 x 10^23 particles per mole.
So energy changes is
E x 6.02 x 10^23 J/mole
or
E x 6.02 x 10^20 kJ/mole
Well, well, well, if it isn't a question about photons and their shenanigans! Alright, let's see what we can do here.
First things first, to calculate the energy change resulting from the emission of photons, we need to find the energy of each individual photon. We can do that using the following equation:
E = hc/λ
Where E is the energy of the photon, h is Planck's constant (6.62607015 × 10^-34 J·s), c is the speed of light (2.998 × 10^8 m/s), and λ is the wavelength of the light.
Now, let's plug in the numbers and see what we get:
E = (6.62607015 × 10^-34 J·s)(2.998 × 10^8 m/s)/(610 × 10^-9 m)
E ≈ 3.2521 × 10^-23 J
Great! Now we have the energy of one single photon. But we want to know the energy change resulting from the emission of 1.00 mol of photons, so we need to multiply this value by Avogadro's number (6.022 × 10^23 mol^-1) to find the energy change per mole:
Energy change = (3.2521 × 10^-23 J)(6.022 × 10^23 mol^-1)
Energy change ≈ 1.96 kJ/mol
Ta-da! The energy change resulting from the emission of 1.00 mol of photons at a wavelength of 610 nm is approximately 1.96 kJ/mol. Hope that brightens up your day!
To calculate the energy change resulting from the emission of photons, we can use the equation:
E = hc/λ
Where:
E is the energy of a single photon
h is Planck's constant (6.62607015 × 10^-34 J·s)
c is the speed of light (2.998 × 10^8 m/s)
λ is the wavelength of the emitted light in meters
First, let's convert the wavelength from nanometers to meters:
610 nm = 610 × 10^-9 m
Now that we have the wavelength in meters, we can calculate the energy of a single photon:
E = (6.62607015 × 10^-34 J·s) × (2.998 × 10^8 m/s) / (610 × 10^-9 m)
E = 3.243 × 10^-19 J
Since we want to calculate the energy change resulting from the emission of 1.00 mol of photons, we need to multiply the energy of a single photon by Avogadro's number (6.022 × 10^23 mol^-1):
Energy change = (3.243 × 10^-19 J) × (6.022 × 10^23 mol^-1)
Energy change = 1.953 kJ/mol
Therefore, the energy change resulting from the emission of 1.00 mol of photons at a wavelength of 610 nm is approximately 1.953 kJ/mol.
To calculate the energy change resulting from the emission of 1.00 mol of photons at a specific wavelength, we need to use the equation:
E = hc/λ
where E is the energy of a photon, h is Planck's constant (6.626 x 10^-34 J*s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the light in meters.
First, we need to convert the wavelength from nm (nanometers) to meters. Since 1 nm = 1 x 10^-9 m, we can convert 610 nm to meters:
λ = 610 nm x (1 x 10^-9 m/1 nm) = 6.10 x 10^-7 m
Now, we can substitute the values into the equation:
E = (6.626 x 10^-34 J*s) x (3.00 x 10^8 m/s) / (6.10 x 10^-7 m)
Calculating this will give us the energy of one photon. However, we want to find the energy change resulting from the emission of 1.00 mol of photons. Since there are Avogadro's number (6.022 x 10^23) of particles in 1.00 mol, we can simply multiply the energy of one photon by Avogadro's number:
Energy change = E x (6.022 x 10^23)
This will give us the energy change in joules. To convert it to kJ, we divide by 1000:
Energy change (kJ/mol) = Energy change (J/mol) / 1000
By performing these calculations, you will find the energy change resulting from the emission of 1.00 mol of photons at a wavelength of 610 nm in units of kJ/mol.