How much energy is contained in 1 mol of each of the following?
X-ray photons with a wavelength of 0.175 nm.
Gamma-ray photons with a wavelength of 2.48×10^−5 nm.
for each photon
E=planck's constant* speedlight/wavelength
find that,then multiply by avag number.
23
To calculate the energy contained in photons, we can use the equation:
E = (hc) / λ
Where:
E is the energy of the photon,
h is Planck's constant (6.626 × 10^-34 J·s),
c is the speed of light (3.00 × 10^8 m/s),
and λ is the wavelength of the photon.
For the first case:
Wavelength (λ) = 0.175 nm = 1.75 × 10^-10 m
Using the equation:
E = (6.626 × 10^-34 J·s × 3.00 × 10^8 m/s) / (1.75 × 10^-10 m)
Calculating, we find:
E = 3.58 × 10^-16 J
Therefore, the energy contained in one mole (6.022 × 10^23) of X-ray photons with a wavelength of 0.175 nm is:
(3.58 × 10^-16 J) × (6.022 × 10^23) ≈ 2.16 × 10^8 J.
For the second case:
Wavelength (λ) = 2.48 × 10^−5 nm = 2.48 × 10^-17 m
Using the equation:
E = (6.626 × 10^-34 J·s × 3.00 × 10^8 m/s) / (2.48 × 10^-17 m)
Calculating, we find:
E = 8.46 × 10^-9 J
Therefore, the energy contained in one mole (6.022 × 10^23) of gamma-ray photons with a wavelength of 2.48 × 10^-5 nm is:
(8.46 × 10^-9 J) × (6.022 × 10^23) ≈ 5.09 × 10^15 J.
So, the energy contained in 1 mole of X-ray photons with a wavelength of 0.175 nm is approximately 2.16 × 10^8 J, and the energy contained in 1 mole of gamma-ray photons with a wavelength of 2.48×10^−5 nm is approximately 5.09 × 10^15 J.
To calculate the energy contained in 1 mol of photons, you can use the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (2.998 x 10^8 m/s), and λ is the wavelength.
Let's start with the X-ray photons with a wavelength of 0.175 nm.
1. Convert the wavelength from nanometers (nm) to meters (m):
0.175 nm = 0.175 x 10^(-9) m
2. Substitute the values into the equation:
E = (6.626 x 10^-34 J·s) x (2.998 x 10^8 m/s) / (0.175 x 10^(-9) m)
3. Calculate the energy:
E = 1.136 x 10^-15 J
Therefore, 1 mol of X-ray photons with a wavelength of 0.175 nm contains 1.136 x 10^-15 J of energy.
Now let's calculate the energy for the gamma-ray photons with a wavelength of 2.48×10^−5 nm.
1. Convert the wavelength from nanometers (nm) to meters (m):
2.48 x 10^(-5) nm = 2.48 x 10^(-5) x 10^(-9) m
2. Apply the equation:
E = (6.626 x 10^-34 J·s) x (2.998 x 10^8 m/s) / (2.48 x 10^(-5) x 10^(-9) m)
3. Calculate the energy:
E = 8.02 x 10^-13 J
Therefore, 1 mol of gamma-ray photons with a wavelength of 2.48×10^−5 nm contains 8.02 x 10^-13 J of energy.