An experiment is set up in which a copper surface is irradiated with high-intensity photons with a wavelength of 15.0nm. Electrons ejected from the surface are found to have a velocity of .548% of c. What is the binding energy of copper's most weakly bound electrons? What is the wavelength of a the lowest-energy photon which can free electrons from copper atoms? Please explain what i need to do, and what equation i have to use because this question is confusing me.

To find the binding energy of copper's most weakly bound electrons, we need to use the equation:

E = hc/λ - φ

Where:
E is the energy of the photon,
h is Planck's constant (6.626 x 10^-34 J·s),
c is the speed of light in a vacuum (3.00 x 10^8 m/s),
λ is the wavelength of the photon,
φ is the binding energy (or work function) of the material.

In this case, the wavelength of the high-intensity photon is given as 15.0 nm (or 15.0 x 10^-9 m), and the velocity of the ejected electrons is given as 0.548% of the speed of light.

To find the velocity of the electron, we can use the equation:

v = βc

Where:
v is the velocity of the electron,
β is the velocity of the electron as a fraction of the speed of light,
c is the speed of light in a vacuum.

Since we know that the velocity is 0.548% of c, we can calculate it using:

v = (0.548/100) * c

Once we have the velocity of the electron, we can calculate its energy using:

E = (1/2)mv^2

Where:
E is the energy of the electron,
m is the mass of the electron.

The mass of an electron is approximately 9.10938356 × 10^-31 kg.

Now that we have the energy of the ejected electron, we can calculate the binding energy by rearranging the first equation:

φ = hc/λ - E

Substituting the values we have, we can determine the binding energy.

To find the wavelength of the lowest-energy photon that can free electrons from copper atoms, we need the binding energy (φ). We can rearrange the equation:

E = hc/λ - φ

To solve for λ, we rewrite the equation as:

λ = hc/(E + φ)

We can then substitute the values for E and φ into the equation to calculate the wavelength.

Remember to use consistent units (e.g., meters) throughout the calculations.