Question

The threshold frequency to describes the smallest light frequency capable of ejecting electrons from a metal. Determine the minimam energy E0​ of a photon capable of ejecting electrons from a metal with ν0​=4,83×1014 s−1. E0​= 3 What is the maxinvam kinetic energy KEdoves ​ of electroes ejected from this metal by light with a wavelength of 265 nm ? KEshoven ​=

Answer 1

The maximum kinetic energy (KE_max) of the electrons ejected from this metal by light with a wavelength of 265 nm is approximately 4.276 x 10^(-19) joules.

To calculate the maximum kinetic energy (KE_max) of electrons ejected from a metal by light with a wavelength of 265 nm, you can use the photoelectric effect equation, which relates the energy of a photon to the work function (Φ) and the maximum kinetic energy of emitted electrons:

KE_max = E_photon - Φ

Where:

- KE_max is the maximum kinetic energy of the emitted electrons.

- E_photon is the energy of the incident photon.

- Φ is the work function of the metal.

First, let's calculate the energy of the photon with the given wavelength (λ = 265 nm) using the speed of light (c = 3.00 x 10^8 m/s) and Planck's constant (h = 6.626 x 10^(-34) J·s):

E_photon = h * (c / λ)

Convert the wavelength to meters:

λ = 265 nm = 265 x 10^(-9) m

Now, calculate E_photon:

E_photon = (6.626 x 10^(-34) J·s) * (3.00 x 10^8 m/s) / (265 x 10^(-9) m)

E_photon ≈ 7.480 x 10^(-19) J

Now, the mentioned threshold frequency (ν0) of the metal as 4.83 x 10^14 s^(-1). The threshold frequency represents the minimum frequency required to eject electrons from the metal, and it is related to the work function (Φ) by the equation:

Φ = h * ν0

Now, calculate Φ:

Φ = (6.626 x 10^(-34) J·s) * (4.83 x 10^14 s^(-1))

Φ ≈ 3.204 x 10^(-19) J

Now that we have Φ, we can calculate the maximum kinetic energy (KE_max) of the ejected electrons:

KE_max = E_photon - Φ

KE_max ≈ (7.480 x 10^(-19) J) - (3.204 x 10^(-19) J)

KE_max ≈ 4.276 x 10^(-19) J

So, the maximum kinetic energy (KE_max) of the electrons ejected from this metal by light with a wavelength of 265 nm is approximately 4.276 x 10^(-19) joules.

Answer 2

The minimum energy is 3.2 *
`10^{-19` J. The kinetic energy is 4.3 *
`10^{-19` J.

The work function represents the energy barrier that must be overcome to liberate electrons. Mathematically, it is the difference between the energy of an incident photon and the energy required to free the electron.

We know that;

Eo = hvo

Eo =
`6.6 * 10^(-34) * 4.83*10^{14`

W = 3.2 *
`10^{-19` J

Energy of the photon = hc/λ

E = 6.6 *
`10^{-34` * 3 *
`10^8`/265 *
`10^{-9`

E = 7.5 *
`10^{-19` J

KE = 7.5 *
`10^{-19` J - 3.2 *
`10^{-19` J

= 4.3 *
`10^{-19` J

This is the kinetic energy