Celiadelacruz
contestada

a bright violet line occurs at 435.8 nm in the emission spectrum of mercury vapor. What amount of energy, in joules, must be released by an electron in a mercury atom to produce a photon of this light?

Respuesta :

nkirotedoreen46

Answer:

4.56 × 10^-19 Joules

Explanation:

We are given;

  • Wavelength of the wave as 435.8 nm

We are required to calculate the amount of energy released by an electron.

  • We know that the speed of the wave, c is 2.998 × 10^8 m/s
  • But, c = f × λ , where f is the frequency and λ is the wavelength
  • Energy of a wave is given by the formula;

E = hf , where h is the plank's constant, 6.626 × 10^-34 J-s

But, f = c/λ

Therefore;

f = (2.998 × 10^8 m/s) ÷ (4.358 × 10^-7 m)

  = 6.879 × 10^14 Hz

Thus;

Energy = 6.626 × 10^-34 J-s ×6.879 × 10^14 Hz

            = 4.558 × 10^-19 Joules

            =  4.56 × 10^-19 Joules

Therefore, the energy that must be released by the electron is 4.56 × 10^-19 Joules

A wavelength is a movement and the distance travelled by a wave with repetition in shape over time. The energy that must be released is [tex]4.56 \times 10^{-19}\;\rm Joules.[/tex]

What is energy?

The energy of the photon is given as the product of Planck's constant and frequency while frequency is the ratio of the speed of light to the wavelength of the photon.

The frequency is given by,

[tex]\rm \nu = \rm \dfrac{c}{\lambda}[/tex]

Where wavelength = 435.8 nm and speed of light = [tex]2.998 \times 10^{8} \;\rm m/s[/tex]

Substituting values in the above equation:

[tex]\begin{aligned} \rm \nu &= \dfrac{2.998 \times 10^{8}}{4.358\times 10^{-7}}\\\\&= 6.87 \times 10^{14}\;\rm Hz\end{aligned}[/tex]

Now, substitute values of the frequency in the energy formula:

[tex]\begin{aligned}\rm E &= \rm h\nu\\\\&=6.626 \times 10^{-34} \;\rm J\;s \times 6.879 \times 10^{14}\;\rm Hz\\\\&= 4.56 \times 10^{-19}\;\rm Joules\end{aligned}[/tex]

Therefore, the energy released by the electron is [tex]4.56 \times 10^{-19}\;\rm Joules.[/tex]

Learn more about energy and frequency here:

https://brainly.com/question/24630281

Otras preguntas