Question

What is the energy in joules of a mole of photons associated with visible light of wavelength 486 nm?

Answer 1

Answer:

$2.46\cdot 10^5 J$

Explanation:

The energy of a single photon is given by:

$E=\frac{hc}{\lambda}$

where

h is the Planck constant

c is the speed of light

$\lambda$ is the wavelength

For the photon in this problem,

$\lambda=486 nm=4.86\cdot 10^{-7}m$

So, its energy is

$E_1=\frac{(6.63\cdot 10^{-34} Js)(3\cdot 10^8 m/s)}{4.86\cdot 10^{-7}m}=4.09\cdot 10^{-19} J$

One mole of photons contains a number of photons equal to Avogadro number:

$N_A = 6.022\cdot 10^{23}$

So, the total energy of one mole of photons is

$E=N_A E_1 = (6.022\cdot 10^{23})(4.09\cdot 10^{-19} J)=2.46\cdot 10^5 J$

Answer 2

The energy of a mole of photons associated with the visible light of a wavelength at 486 nm is 2.46 × 10⁵ J

What is the energy of a single photon?

The energy of a single photon is recognized by the symbol E is expressed using the formula E = hc/λ.

where;

• h = Planck's constant =  6.626 x 10⁻³⁴ Js.
• c = speed of light = 3.0 × 10⁸ m/s

• λ = wavelength = 486 nm = 4.86 × 10⁻⁷ m

One photon of visible light contains about 10⁻¹⁹ Joules (i.e. the no of photons/sec in a beam.)

From the given information, the energy of a mole of photons can be computed as:

$\mathbf{E_1 = \dfrac{6.63 \times 10^{-34 } \ Js \times 3\times 10^8 \ m/s }{4.86 \times 10^{-7} \ m}}$

E₁ = 4.09 × 10⁻¹⁹ J

However, recall that 1 mole of photons = Avogadro's number. Thus, the total energy required for one mole of a photon can be expressed as:

$\mathbf{E = N_A \times E_1}$

$\mathbf{E = 6.022 \times 10^{23} \times 4.09\times 10^{-19} \ J }$

E = 2.46 × 10⁵ J

Learn more about the energy of a single photon here:

https://brainly.com/question/1504539