Question

What is the wavelength (in m) of photons with the energy observed at 90.5 kJ/mol? (Plank’s constant = 6.626 x 10-34 J s)

Answer 1

Solution:-

E = hc / λ

Where, E = energy

h = Plank's constant (= 6.626 × 10^-34 J s)

c = speed of light (= 3 × 10⁸ m /s)

λ = Wavelength.

Given : E = 90.5 kJ/mol = 90500 J/mol

Since the energy is for one mole of photons, first we have to fond the energy of a single photon.

Energy (E) of a single photon = (90500) / (6.023 × 10²³) = 1.50 × 10^-19 J

Thus,

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Answer 2

To find the wavelength (λ) of photons with the given energy, we can use the following equation:

Energy (E) = h * c / λ

Where: E = Energy of the photons in joules h = Planck's constant = 6.626 x 10^-34 J s c = Speed of light in a vacuum = 2.998 x 10^8 m/s λ = Wavelength of the photons in meters

First, we need to convert the given energy from kilojoules per mole to joules per photon. Since 1 mole of photons contains Avogadro's number of photons (6.022 x 10^23), we can calculate the energy per photon:

Energy per photon = Energy per mole / Avogadro's number

Energy per photon = 90.5 kJ/mol / (6.022 x 10^23 photons/mol)

Now, let's convert the energy per photon to joules:

Energy per photon = 90.5 kJ/mol * (1000 J / 1 kJ) / (6.022 x 10^23 photons/mol)

Energy per photon ≈ 1.502 x 10^-19 J

Now, we can use the energy value to find the wavelength:

1.502 x 10^-19 J = (6.626 x 10^-34 J s) * (2.998 x 10^8 m/s) / λ

Now, solve for λ:

λ = (6.626 x 10^-34 J s) * (2.998 x 10^8 m/s) / (1.502 x 10^-19 J)

λ ≈ 1.324 x 10^-7 meters

So, the wavelength of photons with the given energy of 90.5 kJ/mol is approximately 1.324 x 10^-7 meters.

Answer 3

To find the wavelength of photons with the given energy, we can use the equation:

Energy = (Planck's constant * speed of light) / wavelength

We need to rearrange this equation to solve for wavelength:

wavelength = (Planck's constant * speed of light) / Energy

Given: Energy = 90.5 kJ/mol = 90.5 * 10^3 J/mol Planck's constant (h) = 6.626 x 10^-34 J s Speed of light (c) = 3.00 x 10^8 m/s

Now, plug in the values and calculate the wavelength:

wavelength = (6.626 x 10^-34 J s * 3.00 x 10^8 m/s) / (90.5 * 10^3 J/mol)

wavelength ≈ 2.188 x 10^-9 meters

So, the wavelength of the photons with the given energy is approximately 2.188 nanometers (nm).