Question

Certain atoms emit photons of light with an energy of 3.820 ✕ 10−19 J. Calculate the frequency (in Hz) and wavelength (in nm) of one of these photons.

frequency Hz

and

wavelength nm

What is the total energy (in kJ) in 1 mole of these photons?

kJ

Answer 1

The frequency of the photons is 5.766 x 1014 Hz, their wavelength is 520 nm, and the total energy in 1 mole of these photons is 2.300 kJ.

Step-by-step explanation:

To calculate the frequency of the photons using the given energy, you can use the equation that relates energy (E) of a photon to its frequency (f):

E = hf, where h is Planck’s constant (6.626 x 10−34 J·s).

Solving for frequency, we get:

f = E / h = 3.820 x 10−19 J / 6.626 x 10−34 J·s = 5.766 x 1014 Hz.

Next, we calculate the wavelength (λ) using the speed of light (c) and the frequency:

c = λf, where c is the speed of light (3 x 108 m/s).

So, λ = c / f = 3 x 108 m/s / 5.766 x 1014 Hz = 520 nm.

For the total energy of 1 mole of these photons, we use Avogadro's number (NA):

Etotal = NA × E, with NA = 6.022 x 1023 mol−1.

Etotal = 6.022 x 1023 mol−1 × 3.820 x 10−19 J = 2.300 kJ.

Answer 2

ν = 5,765x10¹⁴ Hz

λ = 520 nm

230,0 kJ/mole

Step-by-step explanation:

To convert energy yo frequency you need to use:

E = hν

Where E is energy (3,820x10⁻¹⁹ J)

h is Planck's constant (6,626x10⁻³⁴ Js)

And ν is frequency, replacing ν = 5,765x10¹⁴ s⁻¹ ≡ 5,765x10¹⁴ Hz

To convert frequency to wavelength:

c = λν

Where s is speed of light (2,998x10⁸ ms⁻¹)

ν is frequency (5,765x10¹⁴ s⁻¹)

And λ is wavelength, replacing: λ = 5,200x10⁻⁷ ≡ 520 nm

If 1 photon produce 3,820x10⁻¹⁹ J, in mole of photons produce:

3,820x10⁻¹⁹ J ×
`(6,022x10^(23))/(1 mole)` = 230040 J/mole ≡ 230,0 kJ/mole

I hope it helps!